Why divide by 5 for the variance in this problem?

Conditions

• The dataset is a complete population, not a sample.
• The number of data points $n$ is 5.

Reasoning, step by step

1. Identify the nature of the data from the problem statement: it is a 'population data'.
2. Recall the formula for population variance: $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$.
3. Substitute the number of data points, $n=5$, into the denominator.
4. Conclude that dividing by 5 is correct for calculating the exact variance of this specific population.

Example

The problem stem explicitly writes 'population data' with 5 numbers: 6, 7, 8, 9, 10. The video calculates the variance as $\sigma_1^2 = \frac{10}{5} = 2$, using 5 in the denominator.

Common misconceptions

• Confusing population standard deviation with sample standard deviation, mistakenly thinking the denominators are the same.
• Applying the $n-1$ correction factor (Bessel's correction) to a full population dataset.

Watch the explanation

Connected concepts

Explore next

• How to calculate the standard deviation of a set of population data?
• What is the standard deviation of the data 6, 7, 8, 9, 10?
• When should we divide by n-1 instead of n?