Question

The sample of eight companies in the aerospace industry, referred to in Exercise 36, was surveyed as to their return on investment last year. The results are: 10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6.

. Compute the sample variance.
. Determine the sample standard deviation.

Answer 1

Sample Variance = 6.008

Sample standard deviation = 2.451

Explanation:

We are given the following in the question:

10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, 15.6

Formula:

`\text{Variance} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}`

where
`x_i` are data points,
`\bar{x}` is the mean and n is the number of observations.

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`Mean =\displaystyle(110.8)/(8) = 13.85`

Sum of squares of differences = 42.06

`s^2 = (42.06)/(7) = 6.008`

Standard Deviation =

`s = √(s^2) = √(6.008) = 2.451`