Population Variance of Dataset {67, 79, 55, 61, 88}

Conditions

• The dataset {67, 79, 55, 61, 88} is treated as the entire population.
• The unit of the data is kilograms, so the variance unit is square kilograms.

Reasoning, step by step

1. Calculate the mean: $\mu = \frac{67+79+55+61+88}{5} = 70$.
2. Calculate the squared deviations: $(67-70)^2=9$, $(79-70)^2=81$, $(55-70)^2=225$, $(61-70)^2=81$, $(88-70)^2=324$.
3. Sum the squared deviations: $9+81+225+81+324 = 720$.
4. Divide by the population size $n=5$: $\sigma^2 = \frac{720}{5} = 144$.

Example

The video explicitly shows the calculation: $\sigma^2 = \frac{1}{5}[(-3)^2+9^2+(-15)^2+(-9)^2+18^2] = \frac{1}{5} \times 720 = 144$.

Common misconceptions

• Calculating the sample variance by dividing by 4 instead of 5, which would give 180.
• Making arithmetic errors in summing the squared deviations.
• Forgetting to square the deviations before summing.

Watch the explanation

Connected concepts

Explore next

• What is the population standard deviation of this dataset?
• Why is the variance 144 and not 180?
• What are the units of the population variance?