What is the standard deviation of the data 6, 7, 8, 9, 10?

Q: What is the standard deviation of the data 6, 7, 8, 9, 10?

The standard deviation of this population dataset is $\sqrt{2}$, which is approximately 1.41. This is found by first calculating the mean (8), then the population variance (2), and finally taking the square root of the variance.

The standard deviation of this population dataset is

\sqrt{2}

, which is approximately 1.41. This is found by first calculating the mean (8), then the population variance (2), and finally taking the square root of the variance.

Conditions

The data 6, 7, 8, 9, 10 is treated as a complete population.
The number of data points is 5.

Reasoning, step by step

Calculate the mean: $\frac{6+7+8+9+10}{5} = 8$ .
Calculate the population variance: $\sigma_1^2 = \frac{(6-8)^2+(7-8)^2+(8-8)^2+(9-8)^2+(10-8)^2}{5} = \frac{4+1+0+1+4}{5} = \frac{10}{5} = 2$ .
Calculate the standard deviation by taking the non-negative square root of the variance: $\sigma_1 = \sqrt{2} \approx 1.41$ .

Example

The video displays the three-line solution: Mean = 8; $\sigma_1^2 = 2$ ; $\sigma_1 = \sqrt{2} \approx 1.41$ .

Common misconceptions

Reporting the variance (2) as the final answer instead of the standard deviation ( $\sqrt{2}$ ).
Using the sample variance formula (dividing by 4) which would yield $\sqrt{2.5} \approx 1.58$ .
Rounding intermediate steps incorrectly before taking the final square root.

Watch the explanation

YouTubePopulation standard deviation: a worked example

0:14 – 0:41Watch this moment ↗

Connected concepts

Variance →

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Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.