Question

What is the population standard deviation?

{5,8,8,5}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2

Answer 1

1.5

Explanation:

You want the population standard deviation of the data {5, 8, 8, 5}.

Population variance

The variance of the population is the difference between the mean of ths squares and the square of the mean.

The sum of the squares of the data is ...

5² +8² +8² +5² = 178

So the mean square is 178/4 = 44.5.

The sum of the data is ...

5 +8 + 8 + 5 = 26

so the square of the mean is (26/4)² = 42.25

Then the variance is ...

44.5 -42.25 = 2.25

Standard deviation

The standard deviation is the square root of the variance:

√2.25 = 1.5

The population standard deviation is 1.5.

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Additional comment

Many calculators and spreadsheets can do this math for you. The second attachment shows one such.

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