Question

(b) Use the defining formula to compute the sample standard deviation s. Recall the defining formula used to compute the sample standard deviation s = (x − x)2 n − 1 where x is a member of the data set, x is the mean, and n is number of data values. Before using the formula, we must determine x and n. There are five values in the data set 1, 2, 5, 7, 9, so

n = _______.

Calculate the mean x = x/n by taking the average of the data values, which is dividing the sum of the data values by the number of data values.

x = x /n = ____

1 + 2 + 5 + 7 + 9/_______ =

____/5 =

=

Answer 1

n = 5 (because sample size is 5)

x = x /n = (sum of data value)/n

1 + 2 + 5 + 7 + 9/____5___ =

___24_/5 =

=4.8

So, average is 4.8

Standard deviation calculation

Σ(; – )2 V η -1 (1 – 4.8)2 + (2 – 4.8)2 + (5 – 4.8)2 + (7 – 4.8)2 + (9 – 4.8)2 5 - 1 14.44 + 7.84 + 0.04 + 4.84 + 17.64 44.80 =V 4 = 9,3333333 = 3,055