Question

The ages (in years) and height (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 results.

Height; 79,75,75,71,76,79,73,72,74,71,77,74, Age; 27,26,24,29,25,26,31,27,30,32,36,31.

CV height =

Answer 1

GIVEN:

The two datasets displaying the ages (in years) and height (in inches) of all pitchers for a baseball team:

Age: 27,26,24,29,25,26,31,27,30,32,36,31.

Height: 79,75,75,71,76,79,73,72,74,71,77,74.

Note: I have used excel function to calculate mean and standard deviation of two datasets.

To calculate Mean: "=AVERAGE(select array of data values)"

To calculate Standard deviation: "=STDEV(select array of data values)"

TO FIND:

Coefficient of variation (CV) =?

FORMULA USED:

A coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another. That is,

CALCULATION:

For Dataset Age:

27,26,24,29,25,26,31,27,30,32,36,31.

Mean

Standard deviation

Thus the coefficient of variation for dataset age is,

%

The coefficient of variation for dataset age is %.

For Dataset Height:

79,75,75,71,76,79,73,72,74,71,77,74.

Mean

Standard deviation

Thus the coefficient of variation for dataset age is,

%

The coefficient of variation for dataset age is %.

COMPARISON OF COEFFICIENT OF VARIATION:

The coefficient of variation for dataset age is % and the coefficient of variation for dataset age is %. The coefficient of variation of dataset age is lesser than the coefficient of variation of dataset height. So here it is quite evident that the dispersion is lower in the dataset age when compared to the dataset height.