What is the population standard deviation of the dataset {67, 79, 55, 61, 88}?

Conditions

• The dataset {67, 79, 55, 61, 88} is treated as the entire population.
• The population variance has been correctly calculated as 144.

Reasoning, step by step

1. Identify the population variance $\sigma^2 = 144$.
2. Apply the definition of standard deviation: $\sigma = \sqrt{\sigma^2}$.
3. Calculate the square root: $\sqrt{144} = 12$.
4. Attach the original unit of the data (kilograms) to the result.

Example

The video displays the final step: "The population standard deviation is σ = √$144 = 12$".

Common misconceptions

• Reporting the variance (144) as the standard deviation.
• Taking the negative square root (-12), although standard deviation is defined as non-negative.
• Confusing population standard deviation with sample standard deviation.

Watch the explanation

Connected concepts

Explore next

• How is the standard deviation related to the variance?
• What is the unit of the standard deviation in this problem?
• Why is the standard deviation useful for interpreting the data?