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

Answer:

Sample Variance = 6.008

Sample standard deviation = 2.451

Step-by-step 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.  

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

$Mean =\displaystyle\frac{110.8}{8} = 13.85$

Sum of squares of differences = 42.06

$s^2 = \dfrac{42.06}{7} = 6.008$

Standard Deviation =

$s = \sqrt{s^2} = \sqrt{6.008} = 2.451$