Questions: Calculate the following statistics. Round answers to two decimal places. Statistic Juniors Seniors --------- x̄ 70.14 79.84 s 8.8 6.64 CV Which class has greater variation and why?

Solution Steps

To solve this problem, we need to calculate the coefficient of variation (CV) for both Juniors and Seniors. The CV is calculated as the standard deviation divided by the mean, multiplied by 100 to express it as a percentage. We will then compare the CVs to determine which class has greater variation.

1. Calculate the coefficient of variation (CV) for Juniors using the given mean and standard deviation.
2. Calculate the coefficient of variation (CV) for Seniors using the given mean and standard deviation.
3. Compare the CVs to determine which class has greater variation.

The coefficient of variation (CV) is calculated using the formula: \[ CV = \left( \frac{s}{\bar{x}} \right) \times 100 \] For Juniors: \[ \bar{x}_{\text{Juniors}} = 70.14 \] \[ s_{\text{Juniors}} = 8.8 \] \[ CV_{\text{Juniors}} = \left( \frac{8.8}{70.14} \right) \times 100 \approx 12.55\% \]

For Seniors: \[ \bar{x}_{\text{Seniors}} = 79.84 \] \[ s_{\text{Seniors}} = 6.64 \] \[ CV_{\text{Seniors}} = \left( \frac{6.64}{79.84} \right) \times 100 \approx 8.32\% \]

To determine which class has greater variation, we compare the CVs: \[ CV_{\text{Juniors}} = 12.55\% \] \[ CV_{\text{Seniors}} = 8.32\% \] Since \( CV_{\text{Juniors}} > CV_{\text{Seniors}} \), Juniors have greater variation.

Final Answer