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The following data represents the 2011 guaranteed salaries (in thousands of dollars) of the head coaches of the final 8 teams in the 2011 NCAA Men's Basketball Championship. The data represent the 2011 salaries of basketball coaches of the following universities, entered in that order: Arizona, Butler, Connecticut, Florida, Kansas, Kentucky, North Carolina and Virginia Commonwealth. (Source: www.usatoday.com)
1950 434 2300 3575 3376 3800 1655 418
Compute the range, variance and standard deviation for these data.
Round your answers to the nearest integer, where appropriate.
Answer: Range = 3382
Variance = 1785193
Standard Deviation = 1336
Explanation: Range is the difference between the highest value and lowest value of the set.
Range for the coaches salaries is
range = 3800 - 418
range = 3382
Variance and Standard Deviation are both the statistical measures of the spread between in the data set. In other words, they show how far the numbers in the set are from the mean of the data.
Variance is calculated as
x are the numbers in the set
μ is the mean
n is sample or population quantity
For the coaches' salaries, variance is
s² = 1785192.6
Standard deviation is the squared root of variance:
Then, for coaches' salaries:
s = 1336.11
For the 2011 coaches' salaries, range, variance and standard deviation are 3382, 1785193 and 1336, respectively