what is the standard deviation for the set of values,

Question

25,19,5,21,18,22,17,10,7

Answer 1

Given numbers are 25,19,5,21,18,22,17,10,7

Mean of given numbers  = (25+19+5+21+18+22+17+10+7)/9

= 144/9

= 16

To calculate the given numbers standard deviation, first compute the difference of each data point from the mean,and square the result of each.

(25-16)^2 = 9^2 = 81

(19-16)^2 = (3)^2 = 9

(5-16)^2 = (-11)^2 = 121

(21-16)^2 = 5^2 = 25

(18-16)^2 = 2^2 = 4

(22-16)^2 = 6^2 = 36

(17-16)^2 = 1^2 = 1

(10-16)^2 = (-6)^2 = 36

(7-16)^2 = (-9)^2 = 81

Next compute the mean of these values and take the square root.

Mean = (81+9+121+25+4+36+1+36+81)/9

= 394/9

= 43.77

Sqrt(43.77) = 6.61

standard deviation of given numbers is 6.61.