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The numbers of motor vehicle fatalities in the United States for the years 2010 and 2011 are listed in the table below. Which conclusion is true based on the mean fatalities for the two years?

\begin{tabular}{|l|l|l|}
\hline
Month & 2010 & 2011 \\
\hline
January & 2,290 & 2,365 \\
\hline
February & 2,016 & 2,912 \\
\hline
March & 2,423 & 3,011 \\
\hline
April & 2,777 & 2,638 \\
\hline
May & 2,934 & 2,459 \\
\hline
June & 2,795 & 2,154 \\
\hline
July & 3,095 & 2,268 \\
\hline
August & 3,083 & 2,750 \\
\hline
September & 3,024 & 2,545 \\
\hline
October & 3,056 & 2,323 \\
\hline
November & 2,795 & 2,741 \\
\hline
December & 2,597 & 2,912 \\
\hline
\end{tabular}

A. The variability in the monthly fatalities in 2011 is generally higher than in 2010.

B. The variability in the monthly fatalities in 2010 is equal to the variability in 2011.

C. The monthly fatalities in 2011 are generally higher than in 2010.

D. The monthly fatalities in 2010 are generally higher than in 2011.



Answer :

GinnyAnswer
To answer the question of which conclusion is true based on the mean fatalities for the two years 2010 and 2011, let's follow these steps:

1. Calculate the Mean Fatality Rate for Each Year:
- The mean (or average) is found by summing up all monthly values and then dividing by the number of months.

For 2010:
[tex]\[ \text{Mean of 2010} = \frac{2290 + 2016 + 2423 + 2777 + 2934 + 2795 + 3095 + 3083 + 3024 + 3056 + 2795 + 2597}{12} = 2740.4167 \][/tex]

For 2011:
[tex]\[ \text{Mean of 2011} = \frac{2365 + 2912 + 3011 + 2638 + 2459 + 2154 + 2268 + 2750 + 2545 + 2323 + 2741 + 2912}{12} = 2589.8333 \][/tex]

2. Interpret the Means Comparison:
- We compare the mean values for both years. The mean of 2010 is approximately 2740.4167, and the mean of 2011 is approximately 2589.8333.
- Since 2740.4167 (mean 2010) is greater than 2589.8333 (mean 2011), we can determine that the monthly fatalities in 2010 are generally higher than in 2011.

Therefore, based on the mean fatalities calculated for the two years, the correct conclusion is:

D. The monthly fatalities in 2010 are generally higher than in 2011.

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