sample variance

Question

5

-5

5

-5

-5

14

5

Calculate the value of the sample variance. Round your answer to one decimal place.

Answer 1

three 5's, three -5's, one 14, 7 total numbers

mean is sum of all numbers divided by total number of numbers: 14/7 = 2

find the difference of each number from the mean:, then square that difference:

5-2 = 3, 3^2 = 9

-5-2 = -7, (-7)^2 = 49

14 -2 = 12, 12^2 = 144

sum of squares = 3(9) + 3(49) + 144 = 27 + 147 + 144 = 318

divide by n-1 = 7-1 = 6

318/6 = 53

take the square root

standard deviation = sqr53 = about 7.28

formula for S.D = sqr(sum of squared differences from the mean, all divided by N-1)

had it been a the population, instead of a sample, you'd divide by N instead of N-1.

S.D = 7.3 rounded to one decimal place