Question

Calculate the standard deviation for the following set of numbers: 73, 76, 79, 82, 84, 84, 97

Answer 1

Standard deviation is 7.16

Explanation:

We have given a set of numbers :

73, 76, 79, 82, 84, 84, 97

To calculate the standard deviation of the given data set, first we have to work out the mean.

Mean =
`((73+76+79+82+84+84+97))/(7)`

=
`(575)/(7)` = 82.14

Now for each number subtract the mean and square the result

(73 - 82.14)² = (-9.14)² = 83.54

(76 - 82.14)² = (-6.14)² = 37.70

(79 - 82.14)² = (-3.14)² = 9.86

(82 - 82.14)² = (0.14)² = 0.02

(84 - 82.14)² = (1.86)² = 3.46

(84 - 82.14)² = (1.86)² = 3.46

(97 - 82.14)² = (14.86)²= 220.82

Now we calculate the mean from of those squared differences :

Mean =
`(83.54+37.70+9.86+0.02+3.46+3.46+220.82)/(7)`

=
`(358.86)/(7)`

= 51.27

Now square root of this mean = standard deviation = √51.27 = 7.16

Therefore, Standard deviation is 7.16