Variance of a Dataset
Variance measures how spread out the values in a dataset are around the mean. For a dataset, the main idea is to find the average squared distance from the mean.
Method
- Find the mean of the dataset.
Add all values, then divide by the number of values.
- Find each deviation from the mean.
Subtract the mean from each data value.
- Square each deviation.
Squaring removes negatives and emphasizes larger differences.
- Add the squared deviations.
- Divide by the correct count.
Use the rule given in the exercise or the usual variance rule for that dataset.
- Simplify the result as much as possible.
Good check
- The variance should never be negative.
- If every value in the dataset is the same, the variance is 0.
- Recompute the mean and one or two deviations to make sure the arithmetic is consistent.
Tip
Keep fractions or decimals exact until the end if possible. That helps avoid rounding errors and makes the final simplified answer more reliable.