Question

The ages (in years) and heights (in inches) of all pitchers for a baseball team are listed Find the coefficient of variation for each of the two data sets. Then compare the results

Heights:
73, 77, 74, 76, 79, 78, 79, 70, 72, 71, 79, 79
Ages:
23, 28,28, 27, 27, 29, 26, 28, 30, 37, 36,33

CVheights= %

Answer 1

To find the coefficient of variation (CV) for each of the two data sets, we need to first calculate the standard deviation and mean for each set. Then we can use the formula:

CV = (standard deviation / mean) x 100%

For the heights data set, we have:

Mean height = (73+77+74+76+79+78+79+70+72+71+79+79) / 12 = 75.58 inches

Standard deviation of height = 3.44 inches

Using the formula above, we get:

CVheights = (3.44 / 75.58) x 100% ≈ 4.55%

For the ages data set, we have:

Mean age = (23+28+28+27+27+29+26+28+30+37+36+33) / 12 = 30.5 years

Standard deviation of age = 5.53 years

Using the formula above, we get:

CVages = (5.53 / 30.5) x 100% ≈ 18.13%

Comparing the results, we see that the coefficient of variation for heights is much smaller than that for ages. This suggests that the heights of the pitchers are more tightly clustered around the mean than their ages. In other words, the heights of the pitchers are less variable than their ages.