Question

All 6 members of a family work. their hourly wages (in dollars) are the following.
18, 14, 35, 34, 11, 26
assuming that these wages constitute an entire population, find the standard deviation of the population. round your answer to two decimal places.

Answer 1

The standard deviation of the population dataset is 9.35

How to determine the standard deviation?

The dataset is given as:

18, 14, 35, 34, 11, 26

Start by calculating the mean using:

Mean = Sum/Count

This gives:

$\bar x = (18+ 14+ 35+ 34+ 11+ 26)/6$

Evaluate

$\bar x = 23$

The standard deviation is then calculated using:

$\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n}}$

This gives

$\sigma = \sqrt{\frac{(18 - 23)^2 + (14- 23)^2 + (35- 23)^2 + (34- 23)^2 + (11- 23)^2 + (26- 23)^2}{6}}$

Evaluate

$\sigma = \sqrt{\frac{524}{6}}$

This gives

$\sigma = 9.35$

Hence, the standard deviation of the population is 9.35

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