## The sample of eight companies in the aerospace industry, referred to in Exercise 36, was surveyed as to their return on investment last year

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.

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4 months 2022-01-08T09:34:58+00:00 1 Answer 0 views 0

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 =

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