Mixing
Is mean a better indicator than median in measuring mass shooting?
Clash Royale CLAN TAG#URR8PPP
up vote
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https://skeptics.stackexchange.com/questions/42384/does-america-not-lead-the-world-in-mass-shootings/42460?noredirect=1#comment186132_42460
In that question, someone says that US does not lead in mass shooting. There are more people that are victims of mass shooting per people year in Norway than in US.
I totally agree. Just like the number says.
https://www.snopes.com/fact-check/united-states-lower-death-shootings/
However, disagree. It says that we need to look at median.
I disagree.
I think mean should be the one people look at and not median.
Others disagree.
My answer there is heavily downvoted.
The median value of start up return is negative. But the mean is
positive and that's why we have venture capitalists.
This data is useful for mainly 2 kind of decisions. Does gun right
makes you safer? Is vacationing or living in US is safer than in
Norway. The answer to both is yes, just like the data shows.
Imagine I am tourist. Say I want to know at what place I am more
likely to get shot? In US or in Norway?
The fact that in Norway more people died per capita during mass
shooting is an indicator that I am more likely to die in Norway than
in US.
The fact that in Norway it happens only in 1 year doesn't matter. The
probability is already low enough. Having smaller population, it makes
sense that death rate due to mass shooting in Norway doesn't have to
be big.
My understanding, is the report in https://www.snopes.com/fact-check/united-states-lower-death-shootings/ is neither false or misleading.
US is indeed safer than mass shooting than many countries.
Because the mean is lower.
The median is irrelevant.
That means a tourist planning to go to US will have lower chance of being victim of mass shooting than a tourist planning to go to Norway, because US has lower means.
What do you think?
means
edited 1 hour ago
Phil H
2,6612311
asked 3 hours ago
J. Chang
7901614
add a comment |Â
up vote
2
down vote
favorite
https://skeptics.stackexchange.com/questions/42384/does-america-not-lead-the-world-in-mass-shootings/42460?noredirect=1#comment186132_42460
In that question, someone says that US does not lead in mass shooting. There are more people that are victims of mass shooting per people year in Norway than in US.
I totally agree. Just like the number says.
https://www.snopes.com/fact-check/united-states-lower-death-shootings/
However, disagree. It says that we need to look at median.
I disagree.
I think mean should be the one people look at and not median.
Others disagree.
My answer there is heavily downvoted.
The median value of start up return is negative. But the mean is
positive and that's why we have venture capitalists.
This data is useful for mainly 2 kind of decisions. Does gun right
makes you safer? Is vacationing or living in US is safer than in
Norway. The answer to both is yes, just like the data shows.
Imagine I am tourist. Say I want to know at what place I am more
likely to get shot? In US or in Norway?
The fact that in Norway more people died per capita during mass
shooting is an indicator that I am more likely to die in Norway than
in US.
The fact that in Norway it happens only in 1 year doesn't matter. The
probability is already low enough. Having smaller population, it makes
sense that death rate due to mass shooting in Norway doesn't have to
be big.
My understanding, is the report in https://www.snopes.com/fact-check/united-states-lower-death-shootings/ is neither false or misleading.
US is indeed safer than mass shooting than many countries.
Because the mean is lower.
The median is irrelevant.
That means a tourist planning to go to US will have lower chance of being victim of mass shooting than a tourist planning to go to Norway, because US has lower means.
What do you think?
means
edited 1 hour ago
Phil H
2,6612311
asked 3 hours ago
J. Chang
7901614
The main reason we often decide to look at the median instead of the mean is that the median tends to exclude extreme values in skewed distributions. Essentially ignoring the outliers. For example, if there is a single neighborhood with a high rate, that could skew the mean very heavily, while the median would not be affected.
– ÃÂlon Djurinsky
2 hours ago
This question cannot, to my understanding, be adequately answered based purely on a formal understanding of statistics (which has its own SE site) or mathematics in general; therefore, unless you have a defence, I feel I must vote to close it as primarily opinion-based, despite the merit it has as a question per se.
– Chase Ryan Taylor
2 hours ago
There are plenty of reasons why you might choose one over the other and it is important in my opinion to communicate which is being presented or used in a statistic. Compare a fictional city who every saturday has a mass shooting where 1000 people die but no other shootings to another fictional city where there is never any mass shooting. The median number of deaths per day is zero for both cities, but the first most should agree is certainly more dangerous.
– JMoravitz
2 hours ago
I think if you want to evaluate your chances of being shot in another country compared to the US, you should look at all shooting statistics and not just mass shootings. Also, the Norway statistic is somewhat skewed by a single event in which 77 people were killed. My opinion is that statistics are misused by both sides of the gun violence issue and haggling over whther to use mean or median is nothing more than an attempt to distort a truer meaning of the data.
– Phil H
2 hours ago
Peripheral to the mathematics question, but this question misrepresents the data under discussion. The report cited defines its scope in a way that excludes two-thirds of mass shootings in the USA, so citing it as data on "mass shootings" without qualifier is inaccurate.
– Geoffrey Brent
1 hour ago
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
https://skeptics.stackexchange.com/questions/42384/does-america-not-lead-the-world-in-mass-shootings/42460?noredirect=1#comment186132_42460
In that question, someone says that US does not lead in mass shooting. There are more people that are victims of mass shooting per people year in Norway than in US.
I totally agree. Just like the number says.
https://www.snopes.com/fact-check/united-states-lower-death-shootings/
However, disagree. It says that we need to look at median.
I disagree.
I think mean should be the one people look at and not median.
Others disagree.
My answer there is heavily downvoted.
The median value of start up return is negative. But the mean is
positive and that's why we have venture capitalists.
This data is useful for mainly 2 kind of decisions. Does gun right
makes you safer? Is vacationing or living in US is safer than in
Norway. The answer to both is yes, just like the data shows.
Imagine I am tourist. Say I want to know at what place I am more
likely to get shot? In US or in Norway?
The fact that in Norway more people died per capita during mass
shooting is an indicator that I am more likely to die in Norway than
in US.
The fact that in Norway it happens only in 1 year doesn't matter. The
probability is already low enough. Having smaller population, it makes
sense that death rate due to mass shooting in Norway doesn't have to
be big.
My understanding, is the report in https://www.snopes.com/fact-check/united-states-lower-death-shootings/ is neither false or misleading.
US is indeed safer than mass shooting than many countries.
Because the mean is lower.
The median is irrelevant.
That means a tourist planning to go to US will have lower chance of being victim of mass shooting than a tourist planning to go to Norway, because US has lower means.
What do you think?
means
edited 1 hour ago
Phil H
2,6612311
asked 3 hours ago
J. Chang
7901614
https://skeptics.stackexchange.com/questions/42384/does-america-not-lead-the-world-in-mass-shootings/42460?noredirect=1#comment186132_42460
In that question, someone says that US does not lead in mass shooting. There are more people that are victims of mass shooting per people year in Norway than in US.
I totally agree. Just like the number says.
https://www.snopes.com/fact-check/united-states-lower-death-shootings/
However, disagree. It says that we need to look at median.
I disagree.
I think mean should be the one people look at and not median.
Others disagree.
My answer there is heavily downvoted.
The median value of start up return is negative. But the mean is
positive and that's why we have venture capitalists.
This data is useful for mainly 2 kind of decisions. Does gun right
makes you safer? Is vacationing or living in US is safer than in
Norway. The answer to both is yes, just like the data shows.
Imagine I am tourist. Say I want to know at what place I am more
likely to get shot? In US or in Norway?
The fact that in Norway more people died per capita during mass
shooting is an indicator that I am more likely to die in Norway than
in US.
The fact that in Norway it happens only in 1 year doesn't matter. The
probability is already low enough. Having smaller population, it makes
sense that death rate due to mass shooting in Norway doesn't have to
be big.
My understanding, is the report in https://www.snopes.com/fact-check/united-states-lower-death-shootings/ is neither false or misleading.
US is indeed safer than mass shooting than many countries.
Because the mean is lower.
The median is irrelevant.
That means a tourist planning to go to US will have lower chance of being victim of mass shooting than a tourist planning to go to Norway, because US has lower means.
What do you think?
means
means
edited 1 hour ago
Phil H
2,6612311
asked 3 hours ago
J. Chang
7901614
edited 1 hour ago
Phil H
2,6612311
asked 3 hours ago
J. Chang
7901614
edited 1 hour ago
Phil H
2,6612311
edited 1 hour ago
Phil H
2,6612311
edited 1 hour ago
Phil H
2,6612311
2,6612311
asked 3 hours ago
J. Chang
7901614
asked 3 hours ago
J. Chang
7901614
asked 3 hours ago
J. Chang
7901614
7901614
The main reason we often decide to look at the median instead of the mean is that the median tends to exclude extreme values in skewed distributions. Essentially ignoring the outliers. For example, if there is a single neighborhood with a high rate, that could skew the mean very heavily, while the median would not be affected.
– ÃÂlon Djurinsky
2 hours ago
This question cannot, to my understanding, be adequately answered based purely on a formal understanding of statistics (which has its own SE site) or mathematics in general; therefore, unless you have a defence, I feel I must vote to close it as primarily opinion-based, despite the merit it has as a question per se.
– Chase Ryan Taylor
2 hours ago
There are plenty of reasons why you might choose one over the other and it is important in my opinion to communicate which is being presented or used in a statistic. Compare a fictional city who every saturday has a mass shooting where 1000 people die but no other shootings to another fictional city where there is never any mass shooting. The median number of deaths per day is zero for both cities, but the first most should agree is certainly more dangerous.
– JMoravitz
2 hours ago
I think if you want to evaluate your chances of being shot in another country compared to the US, you should look at all shooting statistics and not just mass shootings. Also, the Norway statistic is somewhat skewed by a single event in which 77 people were killed. My opinion is that statistics are misused by both sides of the gun violence issue and haggling over whther to use mean or median is nothing more than an attempt to distort a truer meaning of the data.
– Phil H
2 hours ago
Peripheral to the mathematics question, but this question misrepresents the data under discussion. The report cited defines its scope in a way that excludes two-thirds of mass shootings in the USA, so citing it as data on "mass shootings" without qualifier is inaccurate.
– Geoffrey Brent
1 hour ago
add a comment |Â
The main reason we often decide to look at the median instead of the mean is that the median tends to exclude extreme values in skewed distributions. Essentially ignoring the outliers. For example, if there is a single neighborhood with a high rate, that could skew the mean very heavily, while the median would not be affected.
– ÃÂlon Djurinsky
2 hours ago
This question cannot, to my understanding, be adequately answered based purely on a formal understanding of statistics (which has its own SE site) or mathematics in general; therefore, unless you have a defence, I feel I must vote to close it as primarily opinion-based, despite the merit it has as a question per se.
– Chase Ryan Taylor
2 hours ago
There are plenty of reasons why you might choose one over the other and it is important in my opinion to communicate which is being presented or used in a statistic. Compare a fictional city who every saturday has a mass shooting where 1000 people die but no other shootings to another fictional city where there is never any mass shooting. The median number of deaths per day is zero for both cities, but the first most should agree is certainly more dangerous.
– JMoravitz
2 hours ago
I think if you want to evaluate your chances of being shot in another country compared to the US, you should look at all shooting statistics and not just mass shootings. Also, the Norway statistic is somewhat skewed by a single event in which 77 people were killed. My opinion is that statistics are misused by both sides of the gun violence issue and haggling over whther to use mean or median is nothing more than an attempt to distort a truer meaning of the data.
– Phil H
2 hours ago
Peripheral to the mathematics question, but this question misrepresents the data under discussion. The report cited defines its scope in a way that excludes two-thirds of mass shootings in the USA, so citing it as data on "mass shootings" without qualifier is inaccurate.
– Geoffrey Brent
1 hour ago
The main reason we often decide to look at the median instead of the mean is that the median tends to exclude extreme values in skewed distributions. Essentially ignoring the outliers. For example, if there is a single neighborhood with a high rate, that could skew the mean very heavily, while the median would not be affected.
– ÃÂlon Djurinsky
2 hours ago
The main reason we often decide to look at the median instead of the mean is that the median tends to exclude extreme values in skewed distributions. Essentially ignoring the outliers. For example, if there is a single neighborhood with a high rate, that could skew the mean very heavily, while the median would not be affected.
– ÃÂlon Djurinsky
2 hours ago
This question cannot, to my understanding, be adequately answered based purely on a formal understanding of statistics (which has its own SE site) or mathematics in general; therefore, unless you have a defence, I feel I must vote to close it as primarily opinion-based, despite the merit it has as a question per se.
– Chase Ryan Taylor
2 hours ago
This question cannot, to my understanding, be adequately answered based purely on a formal understanding of statistics (which has its own SE site) or mathematics in general; therefore, unless you have a defence, I feel I must vote to close it as primarily opinion-based, despite the merit it has as a question per se.
– Chase Ryan Taylor
2 hours ago
There are plenty of reasons why you might choose one over the other and it is important in my opinion to communicate which is being presented or used in a statistic. Compare a fictional city who every saturday has a mass shooting where 1000 people die but no other shootings to another fictional city where there is never any mass shooting. The median number of deaths per day is zero for both cities, but the first most should agree is certainly more dangerous.
– JMoravitz
2 hours ago
There are plenty of reasons why you might choose one over the other and it is important in my opinion to communicate which is being presented or used in a statistic. Compare a fictional city who every saturday has a mass shooting where 1000 people die but no other shootings to another fictional city where there is never any mass shooting. The median number of deaths per day is zero for both cities, but the first most should agree is certainly more dangerous.
– JMoravitz
2 hours ago
I think if you want to evaluate your chances of being shot in another country compared to the US, you should look at all shooting statistics and not just mass shootings. Also, the Norway statistic is somewhat skewed by a single event in which 77 people were killed. My opinion is that statistics are misused by both sides of the gun violence issue and haggling over whther to use mean or median is nothing more than an attempt to distort a truer meaning of the data.
– Phil H
2 hours ago
I think if you want to evaluate your chances of being shot in another country compared to the US, you should look at all shooting statistics and not just mass shootings. Also, the Norway statistic is somewhat skewed by a single event in which 77 people were killed. My opinion is that statistics are misused by both sides of the gun violence issue and haggling over whther to use mean or median is nothing more than an attempt to distort a truer meaning of the data.
– Phil H
2 hours ago
Peripheral to the mathematics question, but this question misrepresents the data under discussion. The report cited defines its scope in a way that excludes two-thirds of mass shootings in the USA, so citing it as data on "mass shootings" without qualifier is inaccurate.
– Geoffrey Brent
1 hour ago
Peripheral to the mathematics question, but this question misrepresents the data under discussion. The report cited defines its scope in a way that excludes two-thirds of mass shootings in the USA, so citing it as data on "mass shootings" without qualifier is inaccurate.
– Geoffrey Brent
1 hour ago
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
3
down vote
That means a tourist planning to go to US will have lower chance of
being victim of mass shooting than a tourist planning to go to Norway,
because US has lower means.
Extrapolating from recent averages can be a good way to estimate future risk, but only when certain criteria are met. One of those criteria is that we have enough recent data to get a reasonably accurate estimate of the true risk.
In the case of US stats, this criterion is probably satisfied. The USA has enough mass shootings that we can get a pretty good estimate of the rate and lethality of these events, unless something happens to cause a change to those rates (e.g. change to US gun laws).
In the case of Norway, this criterion is not satisfied. We cannot accurately estimate the long-term average frequency or lethality of mass shootings based on just a few years of data. An easy way to see this is to note how much the Norwegian averages change if we were to change the reference period.
Obligatory XKCD:
In such cases, getting a good estimate of future risk becomes a hard problem. There are various methods that can be used (look at longer time periods, pool data from similar countries, look at near-misses, ...) none of which are perfect. Getting into the details would be beyond the scope of this question.
Simply looking at the median deaths/year would not be an accurate predictor of future risk, but then Snopes didn't actually make that claim. What the Snopes article actually says is that the median
can give a far better sense of what is typical... in a typical year
between 2009 and 2015, nobody in Norway was killed in a mass shooting.
Which is absolutely true. It then goes on to note:
This doesn’t tell the full story either, since we can’t erase the fact
that 69 people were killed in a devastating attack in 2011. The more
information we examine, the better our understanding. But what the
median does provide, which the mean does not, is a sense of the
consistency of deaths from mass shootings in a particular country,
over a particular period of time.
Those statements seem pretty reasonable as far as they go. A more thorough analysis would talk more about issues such as prediction variance, but those are more complex and harder to get across to a general audience. Invoking the median is reasonable as a way to show why "average" is unreliable here, even if the median doesn't give the full picture either - something that Snopes acknowledges.
answered 47 mins ago
Geoffrey Brent
1,03247
add a comment |Â
up vote
1
down vote
Neither the mean nor the median is really a good measure to use here.
The issue with the mean is that it assumes both the number of mass shootings and the number of mass deaths are representative of their average behavior. This is not too unreasonable for the number of mass shootings: if there was one mass shooting in $7$ years, it makes sense to take that as an estimate of the rate at which the mass shootings occur.
But using the mean also assumes implicitly that we're saying "the average number of people killed in a mass shooting in Norway is $69$". This is reasoning from one data point. This is not nearly enough data to make such a conclusion.
(If we had the same trend over a longer period of time - say, $70$ years that saw $10$ mass shootings killing $69$ people each - I would support you in using the mean.)
Using the median is nonsense as well. For one thing, it fails to distinguish between literally any non-US country on the list, because all of them have a median of $0$. It also ignores the actual numbers of deaths in those countries completely. If we multiply all the non-US numbers by $100$, their medians don't change, but it's obvious that this should make the non-US countries much more dangerous.
Given the data, I think it's a reasonable hypothesis that the number of deaths due to a mass shooting has roughly the same distribution, no matter the country. (Note that Norway doesn't even have the largest mass shooting on the list - France beats it, as far as I can tell.) So it's reasonable to combine the data to establish the average number of casualties in a mass shooting, and multiply it by the average number of mass shootings per capita. I expect that the US is more dangerous than Norway by this measure, but I haven't done the calculation.
Of course, we can try to find better models; for example, it's plausible that the number of deaths in a mass shooting depends on population density. There's enough data there to check this hypothesis, and if so, the estimates can be adjusted as a result.
answered 2 hours ago
Misha Lavrov
38.9k55196
"if there was one mass shooting in 7 years, it makes sense to take that as an estimate of the rate at which the mass shootings occur." Not at all. If you only observe an event once in all of 7 years, you have no idea how rare it is. For example: between the years of 19x0 and 19x9 I was born once. Therefore, on average I am born once every 10 years.
– Rahul
1 hour ago
I didn't say it was a great estimate; but it's not completely unreasonable.
– Misha Lavrov
1 hour ago
I know that's what you said. I'm saying it is unreasonable. Let's say you applied the same argument the day after the Norway mass shooting. Then you're arguing with a straight face that Norway has a mass shooting every day.
– Rahul
1 hour ago
You're picking your window to find a particular example where the argument goes wrong. Most of the time, it wouldn't.
– Misha Lavrov
1 hour ago
Anyway, for an event that's happened once in seven years, we know how to estimate the error in assuming it happens with probability $frac17$. There is no error analysis to be done for a single data point.
– Misha Lavrov
1 hour ago
 |Â
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2 Answers
2
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2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
That means a tourist planning to go to US will have lower chance of
being victim of mass shooting than a tourist planning to go to Norway,
because US has lower means.
Extrapolating from recent averages can be a good way to estimate future risk, but only when certain criteria are met. One of those criteria is that we have enough recent data to get a reasonably accurate estimate of the true risk.
In the case of US stats, this criterion is probably satisfied. The USA has enough mass shootings that we can get a pretty good estimate of the rate and lethality of these events, unless something happens to cause a change to those rates (e.g. change to US gun laws).
In the case of Norway, this criterion is not satisfied. We cannot accurately estimate the long-term average frequency or lethality of mass shootings based on just a few years of data. An easy way to see this is to note how much the Norwegian averages change if we were to change the reference period.
Obligatory XKCD:
In such cases, getting a good estimate of future risk becomes a hard problem. There are various methods that can be used (look at longer time periods, pool data from similar countries, look at near-misses, ...) none of which are perfect. Getting into the details would be beyond the scope of this question.
Simply looking at the median deaths/year would not be an accurate predictor of future risk, but then Snopes didn't actually make that claim. What the Snopes article actually says is that the median
can give a far better sense of what is typical... in a typical year
between 2009 and 2015, nobody in Norway was killed in a mass shooting.
Which is absolutely true. It then goes on to note:
This doesn’t tell the full story either, since we can’t erase the fact
that 69 people were killed in a devastating attack in 2011. The more
information we examine, the better our understanding. But what the
median does provide, which the mean does not, is a sense of the
consistency of deaths from mass shootings in a particular country,
over a particular period of time.
Those statements seem pretty reasonable as far as they go. A more thorough analysis would talk more about issues such as prediction variance, but those are more complex and harder to get across to a general audience. Invoking the median is reasonable as a way to show why "average" is unreliable here, even if the median doesn't give the full picture either - something that Snopes acknowledges.
answered 47 mins ago
Geoffrey Brent
1,03247
add a comment |Â
up vote
3
down vote
That means a tourist planning to go to US will have lower chance of
being victim of mass shooting than a tourist planning to go to Norway,
because US has lower means.
Extrapolating from recent averages can be a good way to estimate future risk, but only when certain criteria are met. One of those criteria is that we have enough recent data to get a reasonably accurate estimate of the true risk.
In the case of US stats, this criterion is probably satisfied. The USA has enough mass shootings that we can get a pretty good estimate of the rate and lethality of these events, unless something happens to cause a change to those rates (e.g. change to US gun laws).
In the case of Norway, this criterion is not satisfied. We cannot accurately estimate the long-term average frequency or lethality of mass shootings based on just a few years of data. An easy way to see this is to note how much the Norwegian averages change if we were to change the reference period.
Obligatory XKCD:
In such cases, getting a good estimate of future risk becomes a hard problem. There are various methods that can be used (look at longer time periods, pool data from similar countries, look at near-misses, ...) none of which are perfect. Getting into the details would be beyond the scope of this question.
Simply looking at the median deaths/year would not be an accurate predictor of future risk, but then Snopes didn't actually make that claim. What the Snopes article actually says is that the median
can give a far better sense of what is typical... in a typical year
between 2009 and 2015, nobody in Norway was killed in a mass shooting.
Which is absolutely true. It then goes on to note:
This doesn’t tell the full story either, since we can’t erase the fact
that 69 people were killed in a devastating attack in 2011. The more
information we examine, the better our understanding. But what the
median does provide, which the mean does not, is a sense of the
consistency of deaths from mass shootings in a particular country,
over a particular period of time.
Those statements seem pretty reasonable as far as they go. A more thorough analysis would talk more about issues such as prediction variance, but those are more complex and harder to get across to a general audience. Invoking the median is reasonable as a way to show why "average" is unreliable here, even if the median doesn't give the full picture either - something that Snopes acknowledges.
answered 47 mins ago
Geoffrey Brent
1,03247
add a comment |Â
up vote
3
down vote
up vote
3
down vote
That means a tourist planning to go to US will have lower chance of
being victim of mass shooting than a tourist planning to go to Norway,
because US has lower means.
Extrapolating from recent averages can be a good way to estimate future risk, but only when certain criteria are met. One of those criteria is that we have enough recent data to get a reasonably accurate estimate of the true risk.
In the case of US stats, this criterion is probably satisfied. The USA has enough mass shootings that we can get a pretty good estimate of the rate and lethality of these events, unless something happens to cause a change to those rates (e.g. change to US gun laws).
In the case of Norway, this criterion is not satisfied. We cannot accurately estimate the long-term average frequency or lethality of mass shootings based on just a few years of data. An easy way to see this is to note how much the Norwegian averages change if we were to change the reference period.
Obligatory XKCD:
In such cases, getting a good estimate of future risk becomes a hard problem. There are various methods that can be used (look at longer time periods, pool data from similar countries, look at near-misses, ...) none of which are perfect. Getting into the details would be beyond the scope of this question.
Simply looking at the median deaths/year would not be an accurate predictor of future risk, but then Snopes didn't actually make that claim. What the Snopes article actually says is that the median
can give a far better sense of what is typical... in a typical year
between 2009 and 2015, nobody in Norway was killed in a mass shooting.
Which is absolutely true. It then goes on to note:
This doesn’t tell the full story either, since we can’t erase the fact
that 69 people were killed in a devastating attack in 2011. The more
information we examine, the better our understanding. But what the
median does provide, which the mean does not, is a sense of the
consistency of deaths from mass shootings in a particular country,
over a particular period of time.
Those statements seem pretty reasonable as far as they go. A more thorough analysis would talk more about issues such as prediction variance, but those are more complex and harder to get across to a general audience. Invoking the median is reasonable as a way to show why "average" is unreliable here, even if the median doesn't give the full picture either - something that Snopes acknowledges.
answered 47 mins ago
Geoffrey Brent
1,03247
That means a tourist planning to go to US will have lower chance of
being victim of mass shooting than a tourist planning to go to Norway,
because US has lower means.
Extrapolating from recent averages can be a good way to estimate future risk, but only when certain criteria are met. One of those criteria is that we have enough recent data to get a reasonably accurate estimate of the true risk.
In the case of US stats, this criterion is probably satisfied. The USA has enough mass shootings that we can get a pretty good estimate of the rate and lethality of these events, unless something happens to cause a change to those rates (e.g. change to US gun laws).
In the case of Norway, this criterion is not satisfied. We cannot accurately estimate the long-term average frequency or lethality of mass shootings based on just a few years of data. An easy way to see this is to note how much the Norwegian averages change if we were to change the reference period.
Obligatory XKCD:
In such cases, getting a good estimate of future risk becomes a hard problem. There are various methods that can be used (look at longer time periods, pool data from similar countries, look at near-misses, ...) none of which are perfect. Getting into the details would be beyond the scope of this question.
Simply looking at the median deaths/year would not be an accurate predictor of future risk, but then Snopes didn't actually make that claim. What the Snopes article actually says is that the median
can give a far better sense of what is typical... in a typical year
between 2009 and 2015, nobody in Norway was killed in a mass shooting.
Which is absolutely true. It then goes on to note:
This doesn’t tell the full story either, since we can’t erase the fact
that 69 people were killed in a devastating attack in 2011. The more
information we examine, the better our understanding. But what the
median does provide, which the mean does not, is a sense of the
consistency of deaths from mass shootings in a particular country,
over a particular period of time.
Those statements seem pretty reasonable as far as they go. A more thorough analysis would talk more about issues such as prediction variance, but those are more complex and harder to get across to a general audience. Invoking the median is reasonable as a way to show why "average" is unreliable here, even if the median doesn't give the full picture either - something that Snopes acknowledges.
answered 47 mins ago
Geoffrey Brent
1,03247
answered 47 mins ago
Geoffrey Brent
1,03247
answered 47 mins ago
Geoffrey Brent
1,03247
answered 47 mins ago
Geoffrey Brent
1,03247
1,03247
add a comment |Â
add a comment |Â
up vote
1
down vote
Neither the mean nor the median is really a good measure to use here.
The issue with the mean is that it assumes both the number of mass shootings and the number of mass deaths are representative of their average behavior. This is not too unreasonable for the number of mass shootings: if there was one mass shooting in $7$ years, it makes sense to take that as an estimate of the rate at which the mass shootings occur.
But using the mean also assumes implicitly that we're saying "the average number of people killed in a mass shooting in Norway is $69$". This is reasoning from one data point. This is not nearly enough data to make such a conclusion.
(If we had the same trend over a longer period of time - say, $70$ years that saw $10$ mass shootings killing $69$ people each - I would support you in using the mean.)
Using the median is nonsense as well. For one thing, it fails to distinguish between literally any non-US country on the list, because all of them have a median of $0$. It also ignores the actual numbers of deaths in those countries completely. If we multiply all the non-US numbers by $100$, their medians don't change, but it's obvious that this should make the non-US countries much more dangerous.
Given the data, I think it's a reasonable hypothesis that the number of deaths due to a mass shooting has roughly the same distribution, no matter the country. (Note that Norway doesn't even have the largest mass shooting on the list - France beats it, as far as I can tell.) So it's reasonable to combine the data to establish the average number of casualties in a mass shooting, and multiply it by the average number of mass shootings per capita. I expect that the US is more dangerous than Norway by this measure, but I haven't done the calculation.
Of course, we can try to find better models; for example, it's plausible that the number of deaths in a mass shooting depends on population density. There's enough data there to check this hypothesis, and if so, the estimates can be adjusted as a result.
answered 2 hours ago
Misha Lavrov
38.9k55196
"if there was one mass shooting in 7 years, it makes sense to take that as an estimate of the rate at which the mass shootings occur." Not at all. If you only observe an event once in all of 7 years, you have no idea how rare it is. For example: between the years of 19x0 and 19x9 I was born once. Therefore, on average I am born once every 10 years.
– Rahul
1 hour ago
I didn't say it was a great estimate; but it's not completely unreasonable.
– Misha Lavrov
1 hour ago
I know that's what you said. I'm saying it is unreasonable. Let's say you applied the same argument the day after the Norway mass shooting. Then you're arguing with a straight face that Norway has a mass shooting every day.
– Rahul
1 hour ago
You're picking your window to find a particular example where the argument goes wrong. Most of the time, it wouldn't.
– Misha Lavrov
1 hour ago
Anyway, for an event that's happened once in seven years, we know how to estimate the error in assuming it happens with probability $frac17$. There is no error analysis to be done for a single data point.
– Misha Lavrov
1 hour ago
 |Â
show 5 more comments
up vote
1
down vote
Neither the mean nor the median is really a good measure to use here.
The issue with the mean is that it assumes both the number of mass shootings and the number of mass deaths are representative of their average behavior. This is not too unreasonable for the number of mass shootings: if there was one mass shooting in $7$ years, it makes sense to take that as an estimate of the rate at which the mass shootings occur.
But using the mean also assumes implicitly that we're saying "the average number of people killed in a mass shooting in Norway is $69$". This is reasoning from one data point. This is not nearly enough data to make such a conclusion.
(If we had the same trend over a longer period of time - say, $70$ years that saw $10$ mass shootings killing $69$ people each - I would support you in using the mean.)
Using the median is nonsense as well. For one thing, it fails to distinguish between literally any non-US country on the list, because all of them have a median of $0$. It also ignores the actual numbers of deaths in those countries completely. If we multiply all the non-US numbers by $100$, their medians don't change, but it's obvious that this should make the non-US countries much more dangerous.
Given the data, I think it's a reasonable hypothesis that the number of deaths due to a mass shooting has roughly the same distribution, no matter the country. (Note that Norway doesn't even have the largest mass shooting on the list - France beats it, as far as I can tell.) So it's reasonable to combine the data to establish the average number of casualties in a mass shooting, and multiply it by the average number of mass shootings per capita. I expect that the US is more dangerous than Norway by this measure, but I haven't done the calculation.
Of course, we can try to find better models; for example, it's plausible that the number of deaths in a mass shooting depends on population density. There's enough data there to check this hypothesis, and if so, the estimates can be adjusted as a result.
answered 2 hours ago
Misha Lavrov
38.9k55196
"if there was one mass shooting in 7 years, it makes sense to take that as an estimate of the rate at which the mass shootings occur." Not at all. If you only observe an event once in all of 7 years, you have no idea how rare it is. For example: between the years of 19x0 and 19x9 I was born once. Therefore, on average I am born once every 10 years.
– Rahul
1 hour ago
I didn't say it was a great estimate; but it's not completely unreasonable.
– Misha Lavrov
1 hour ago
I know that's what you said. I'm saying it is unreasonable. Let's say you applied the same argument the day after the Norway mass shooting. Then you're arguing with a straight face that Norway has a mass shooting every day.
– Rahul
1 hour ago
You're picking your window to find a particular example where the argument goes wrong. Most of the time, it wouldn't.
– Misha Lavrov
1 hour ago
Anyway, for an event that's happened once in seven years, we know how to estimate the error in assuming it happens with probability $frac17$. There is no error analysis to be done for a single data point.
– Misha Lavrov
1 hour ago
 |Â
show 5 more comments
up vote
1
down vote
up vote
1
down vote
Neither the mean nor the median is really a good measure to use here.
The issue with the mean is that it assumes both the number of mass shootings and the number of mass deaths are representative of their average behavior. This is not too unreasonable for the number of mass shootings: if there was one mass shooting in $7$ years, it makes sense to take that as an estimate of the rate at which the mass shootings occur.
But using the mean also assumes implicitly that we're saying "the average number of people killed in a mass shooting in Norway is $69$". This is reasoning from one data point. This is not nearly enough data to make such a conclusion.
(If we had the same trend over a longer period of time - say, $70$ years that saw $10$ mass shootings killing $69$ people each - I would support you in using the mean.)
Using the median is nonsense as well. For one thing, it fails to distinguish between literally any non-US country on the list, because all of them have a median of $0$. It also ignores the actual numbers of deaths in those countries completely. If we multiply all the non-US numbers by $100$, their medians don't change, but it's obvious that this should make the non-US countries much more dangerous.
Given the data, I think it's a reasonable hypothesis that the number of deaths due to a mass shooting has roughly the same distribution, no matter the country. (Note that Norway doesn't even have the largest mass shooting on the list - France beats it, as far as I can tell.) So it's reasonable to combine the data to establish the average number of casualties in a mass shooting, and multiply it by the average number of mass shootings per capita. I expect that the US is more dangerous than Norway by this measure, but I haven't done the calculation.
Of course, we can try to find better models; for example, it's plausible that the number of deaths in a mass shooting depends on population density. There's enough data there to check this hypothesis, and if so, the estimates can be adjusted as a result.
answered 2 hours ago
Misha Lavrov
38.9k55196
Neither the mean nor the median is really a good measure to use here.
The issue with the mean is that it assumes both the number of mass shootings and the number of mass deaths are representative of their average behavior. This is not too unreasonable for the number of mass shootings: if there was one mass shooting in $7$ years, it makes sense to take that as an estimate of the rate at which the mass shootings occur.
But using the mean also assumes implicitly that we're saying "the average number of people killed in a mass shooting in Norway is $69$". This is reasoning from one data point. This is not nearly enough data to make such a conclusion.
(If we had the same trend over a longer period of time - say, $70$ years that saw $10$ mass shootings killing $69$ people each - I would support you in using the mean.)
Using the median is nonsense as well. For one thing, it fails to distinguish between literally any non-US country on the list, because all of them have a median of $0$. It also ignores the actual numbers of deaths in those countries completely. If we multiply all the non-US numbers by $100$, their medians don't change, but it's obvious that this should make the non-US countries much more dangerous.
Given the data, I think it's a reasonable hypothesis that the number of deaths due to a mass shooting has roughly the same distribution, no matter the country. (Note that Norway doesn't even have the largest mass shooting on the list - France beats it, as far as I can tell.) So it's reasonable to combine the data to establish the average number of casualties in a mass shooting, and multiply it by the average number of mass shootings per capita. I expect that the US is more dangerous than Norway by this measure, but I haven't done the calculation.
Of course, we can try to find better models; for example, it's plausible that the number of deaths in a mass shooting depends on population density. There's enough data there to check this hypothesis, and if so, the estimates can be adjusted as a result.
answered 2 hours ago
Misha Lavrov
38.9k55196
answered 2 hours ago
Misha Lavrov
38.9k55196
answered 2 hours ago
Misha Lavrov
38.9k55196
answered 2 hours ago
Misha Lavrov
38.9k55196
38.9k55196
"if there was one mass shooting in 7 years, it makes sense to take that as an estimate of the rate at which the mass shootings occur." Not at all. If you only observe an event once in all of 7 years, you have no idea how rare it is. For example: between the years of 19x0 and 19x9 I was born once. Therefore, on average I am born once every 10 years.
– Rahul
1 hour ago
I didn't say it was a great estimate; but it's not completely unreasonable.
– Misha Lavrov
1 hour ago
I know that's what you said. I'm saying it is unreasonable. Let's say you applied the same argument the day after the Norway mass shooting. Then you're arguing with a straight face that Norway has a mass shooting every day.
– Rahul
1 hour ago
You're picking your window to find a particular example where the argument goes wrong. Most of the time, it wouldn't.
– Misha Lavrov
1 hour ago
Anyway, for an event that's happened once in seven years, we know how to estimate the error in assuming it happens with probability $frac17$. There is no error analysis to be done for a single data point.
– Misha Lavrov
1 hour ago
 |Â
show 5 more comments
"if there was one mass shooting in 7 years, it makes sense to take that as an estimate of the rate at which the mass shootings occur." Not at all. If you only observe an event once in all of 7 years, you have no idea how rare it is. For example: between the years of 19x0 and 19x9 I was born once. Therefore, on average I am born once every 10 years.
– Rahul
1 hour ago
I didn't say it was a great estimate; but it's not completely unreasonable.
– Misha Lavrov
1 hour ago
I know that's what you said. I'm saying it is unreasonable. Let's say you applied the same argument the day after the Norway mass shooting. Then you're arguing with a straight face that Norway has a mass shooting every day.
– Rahul
1 hour ago
You're picking your window to find a particular example where the argument goes wrong. Most of the time, it wouldn't.
– Misha Lavrov
1 hour ago
Anyway, for an event that's happened once in seven years, we know how to estimate the error in assuming it happens with probability $frac17$. There is no error analysis to be done for a single data point.
– Misha Lavrov
1 hour ago
"if there was one mass shooting in 7 years, it makes sense to take that as an estimate of the rate at which the mass shootings occur." Not at all. If you only observe an event once in all of 7 years, you have no idea how rare it is. For example: between the years of 19x0 and 19x9 I was born once. Therefore, on average I am born once every 10 years.
– Rahul
1 hour ago
"if there was one mass shooting in 7 years, it makes sense to take that as an estimate of the rate at which the mass shootings occur." Not at all. If you only observe an event once in all of 7 years, you have no idea how rare it is. For example: between the years of 19x0 and 19x9 I was born once. Therefore, on average I am born once every 10 years.
– Rahul
1 hour ago
I didn't say it was a great estimate; but it's not completely unreasonable.
– Misha Lavrov
1 hour ago
I didn't say it was a great estimate; but it's not completely unreasonable.
– Misha Lavrov
1 hour ago
I know that's what you said. I'm saying it is unreasonable. Let's say you applied the same argument the day after the Norway mass shooting. Then you're arguing with a straight face that Norway has a mass shooting every day.
– Rahul
1 hour ago
I know that's what you said. I'm saying it is unreasonable. Let's say you applied the same argument the day after the Norway mass shooting. Then you're arguing with a straight face that Norway has a mass shooting every day.
– Rahul
1 hour ago
You're picking your window to find a particular example where the argument goes wrong. Most of the time, it wouldn't.
– Misha Lavrov
1 hour ago
You're picking your window to find a particular example where the argument goes wrong. Most of the time, it wouldn't.
– Misha Lavrov
1 hour ago
Anyway, for an event that's happened once in seven years, we know how to estimate the error in assuming it happens with probability $frac17$. There is no error analysis to be done for a single data point.
– Misha Lavrov
1 hour ago
Anyway, for an event that's happened once in seven years, we know how to estimate the error in assuming it happens with probability $frac17$. There is no error analysis to be done for a single data point.
– Misha Lavrov
1 hour ago
 |Â
show 5 more comments
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The main reason we often decide to look at the median instead of the mean is that the median tends to exclude extreme values in skewed distributions. Essentially ignoring the outliers. For example, if there is a single neighborhood with a high rate, that could skew the mean very heavily, while the median would not be affected.
– ÃÂlon Djurinsky
2 hours ago
This question cannot, to my understanding, be adequately answered based purely on a formal understanding of statistics (which has its own SE site) or mathematics in general; therefore, unless you have a defence, I feel I must vote to close it as primarily opinion-based, despite the merit it has as a question per se.
– Chase Ryan Taylor
2 hours ago
There are plenty of reasons why you might choose one over the other and it is important in my opinion to communicate which is being presented or used in a statistic. Compare a fictional city who every saturday has a mass shooting where 1000 people die but no other shootings to another fictional city where there is never any mass shooting. The median number of deaths per day is zero for both cities, but the first most should agree is certainly more dangerous.
– JMoravitz
2 hours ago
I think if you want to evaluate your chances of being shot in another country compared to the US, you should look at all shooting statistics and not just mass shootings. Also, the Norway statistic is somewhat skewed by a single event in which 77 people were killed. My opinion is that statistics are misused by both sides of the gun violence issue and haggling over whther to use mean or median is nothing more than an attempt to distort a truer meaning of the data.
– Phil H
2 hours ago
Peripheral to the mathematics question, but this question misrepresents the data under discussion. The report cited defines its scope in a way that excludes two-thirds of mass shootings in the USA, so citing it as data on "mass shootings" without qualifier is inaccurate.
– Geoffrey Brent
1 hour ago