Standard deviation of a list of numbers with hints

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Question 1

Find the Standard Deviation

Find the standard deviation of the following list of numbers [ 8, 21, 12, 23, 24, 1, 22, 16 ].

Give your answer correct to one decimal place.

Standard deviation = $\sqrt{\frac{\Sigma (x-\text{mean})^2}{n}}$

To find the standard deviation, first find the mean of the list of numbers.

What is the mean?

Now, subtract the mean individually from each of the numbers given and square the result.

Now add up these results. This is the ' $\Sigma (x-\text{mean})^2$ ' part in the formula.
Divide by $n$ where $n$ is the number of values.

Finally, find the square root.

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Advice

Standard deviation = $\sqrt{\frac{\Sigma (x-\text{mean})^2}{n}}$

What is the mean? Add up the numbers and divide by the number of numbers getting an answer of 15.875.

Now, subtract the mean individually from each of the numbers given and square the result.

Now add up these results. This is the ' $\Sigma (x-\text{mean})^2$ ' part in the formula.
Divide by 8 the number of values. This gives an answer of 59.859375.

Finally, find the square root to get an answer of 7.7368840627.

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Standard deviation of a list of numbers with hints

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