Question: Test scores: Scores on a statistics exam had a mean of 71 with a standard deviation of 6. Scores on…

Test scores: Scores on a statistics exam had a mean of 71 with a standard deviation of 6. Scores on a calculus exam had a mean of 60 with a standard deviation of 10.

Part 1 of 3

(a) Compute the coefficient of variation for statistics exam scores. Round the answer to at least two decimal places.

The coefficient of variation for statistics exam scores is 8.45.

Part 2 of 3

(b) Compute the coefficient of variation for calculus exam scores. Round the answer to at least two decimal places.

The coefficient of variation for calculus exam scores is 16.67.

Part 3 of 3

(c) Which has greater spread relative to their mean, statistics scores or calculus scores?

Choose one has greater spread relative to its mean.

Solution

Test scores: Scores on a statistics exam had a mean of 71 with a standard deviation of 6. Scores on a calculus exam had a mean of 60 with a standard deviation of 10. Part (a) Compute the coefficient of variation for statistics exam scores. The coefficient of variation (CV) is calculated using the formula: \[ CV = \left(\frac{\text{Standard Deviation}}{\text{Mean}}\right) \times 100 \] For the statistics exam: \[ CV = \left(\frac{6}{71}\right) \times 100 \approx 8.45 \] Part (b) Compute the coefficient of variation for calculus exam scores. For the calculus exam: \[ CV = \left(\frac{10}{60}\right) \times 100 \approx 16.67 \] Part (c) Which has greater spread relative to their mean, statistics scores or calculus scores? The calculus scores have a greater spread relative to their mean because the coefficient of variation for calculus scores (16.67) is higher than that for statistics scores (8.45).