Statistics homework

Question

Find the range and standard deviation of the list of scores that were made by a football team during a season.

Scores: 0, 7, 7, 14, 17, 17, 21, 21

                                   Range: _______                     Standard Deviation:

Answer 1

range is largest minus smallest = 21-0= 21

square root is the square root of the variance

variance = average of sum of squared deviations from the mean

mean is the arithmetic average = 104/8= 13

deviations from the mean are -13,- 6,- 6, 1, 4, 4, 8,8

squared deviations are 169, 36, 36, 1, 16, 16, 64, 64

sum of squared deviatios is 402

average = 402/8 = 50.25

square root of average sum of squared deviations from the mean = sqr50.25 = about 7.09

that's true if the data is the whole population

but if the data is a sample then

divide the sum of squared deviations by n-1 = 7

then variance = 402/7 = 57 3/7

standard deviation = about 7.58