High School

The means and mean absolute deviations of the individual times of members on two [tex]4 \times 400[/tex]-meter relay track teams are shown in the table below.

[tex]
\[
\begin{array}{|c|c|c|}
\hline
\multicolumn{3}{|c|}{\text{Means and Mean Absolute Deviations of Individual Times of Members of } 4 \times 400\text{-meter Relay Track Teams}} \\
\hline
& \text{Team A} & \text{Team B} \\
\hline
\text{Mean} & & \\
\hline
\text{Mean Absolute Deviation} & 59.32 \, \text{s} & 59.1 \, \text{s} \\
\hline
\end{array}
\]
[/tex]

What is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B?

A. 0.09

B. 0.15

C. 0.25

D. 0.65

Answer :

To solve the problem, we need to find the ratio of the difference in the means of the two teams to the mean absolute deviation (MAD) of Team B. Let's break down the steps clearly:

1. Identify the Means of Each Team:
- The mean time for Team A is 59.32 seconds.
- The mean time for Team B is 59.1 seconds.

2. Calculate the Difference in Means:
- Subtract the mean of Team B from the mean of Team A:
[tex]\( \text{Difference} = 59.32 - 59.1 = 0.22 \)[/tex] seconds.

3. Identify the Mean Absolute Deviation (MAD) of Team B:
- The MAD for Team B is 0.65 seconds.

4. Calculate the Ratio:
- Divide the difference in means by the MAD of Team B:
[tex]\( \text{Ratio} = \frac{0.22}{0.65} \)[/tex].

5. Simplify the Ratio:
- Calculating the division:
[tex]\( \text{Ratio} \approx 0.338 \)[/tex].

Based on the multiple choice options given:
- 0.09
- 0.15
- 0.25
- 0.65

The closest option to the calculated ratio of approximately 0.338 is not exactly listed, which might suggest a discrepancy. However, since the typical options may contain rounding not mentioned, confirm that the logical steps were correct and if needed, verify the options provided for any rounding interpretations.