The following sites will help deepen your understanding of the data behind the death rate by firearms for males and females. What does the term 'death rate' mean?

View graphics and explanations of various statistics on the rate of firearm violence in this report.

Of course, the United States is not the only country with high rates of firearm injuries and deaths. This report from Australia provides a report on gun injury statistics, with graphics concerning the difference in the rate for males and females.

For a more international perspective, see this graphical report that includes statistics on the firearm death rate for different countries.

Do you find the rate given for the US surprising?

The US Center for Disease Control (CDC) provides some quick statistics on the problem, including graphics and statistical measures.
Also refer to their graph of firearm deaths over time.
The data used in the following analysis also comes from the CDC.

The following graphs show the death rates (deaths per 100,000) by firearms for males and females from 1992 to 1995. The rates are much higher for males than for females, but the question we ask of the data in this project concerns the amount of variation present rather than the actual rates.

Firearm Death Rate, by Sex
firearm deaths plot

firearm deaths boxplot

The Chi-Square Test for a Population Standard Deviation


The standard deviation for the death rate by firearms for males in 1994 is 16.64. Assume, for the sake of the argument, that this is the population standard deviation. From the data given in the following table, the sample standard deviation is 15.07 in 1995. The numbers represent the death rate for different age groups: the first number indicates the death rate for those aged 4 and younger, the second number represents the rate for those aged between 5 and 9 years, etc.

1995: Death by Firearms for Males
0.63 0.68 5.25 42.41 52.81 38.87 30.42 24.48 22.88
20.43 20.31 19.50 20.57 22.57 28.47 34.77 42.63 47.40

The chi-square value for the hypothesis test that the 1995 standard deviation is equal to 16.64 is:

[(17)/16.642]*15.072 = 13.94.

The 95% chi-square value is 27.59. Thus, we cannot reject the null hypothesis (that the standard deviation for 1995 is significantly different from 16.64 at the 95% level).

Comparing Two Population Standard Deviations


Is the standard deviation the same for males and females? The standard deviation for the death rate by firearms for females across all years is 1.86.

1995: Death by Firearms for Females
0.44 0.43 1.43 5.72 6.21 5.89 5.99 5.30 5.20
4.21 4.40 3.57 3.46 3.15 2.86 2.85 2.77 1.80

The standard deviation for males is 15.07. The calculated F value is

15.072/1.862 = 65.64.

The 97.5% F value (with 17, 17 degrees of freedom) is 2.67. The 2.5% F value is 0.374. Thus, we reject the null hypothesis that the standard deviations for males and females are equal, at the 95% level.

What does it mean?

It is interesting that the variability in the male population is so much greater than for the female population. Think for a moment about what it means to have a large variance in the death rate by firearms. Some groups of males have a low death rate and others have a high death rate. Females tend to have a much lower rate across all groups.

As is usual with statistical analysis, it is the examination of variability that shows the interesting phenomena underlying the data. If there was no, or little, variability, there would be little to study.

Often, high volatility of the data will point researchers to important factors behind the data. The fact that males have a high volatility in the death rate by firearms may lead researchers to further studies; to attempt to determine which groups of males have a higher rate and why.