Variance and Standard Deviation

Variance and Standard Deviation

Measures of spread describe how widely data lie around the mean. Variance averages squared deviations; standard deviation is the square root of variance and returns to the original units. A larger standard deviation means data are more spread out. Compare both centre and spread before declaring one group more consistent.

Worked reasoning

Data A and B can have the same mean but different scatter. If A is tightly clustered around its mean, it has a smaller standard deviation and is more consistent than B.

Exam method

1. Find/identify the mean. 2. Read or calculate deviations using the required method. 3. Interpret the size of standard deviation in the original context and units.

Compare like with like

Standard deviation is most useful when two groups measure the same quantity in the same units. Report both the means and standard deviations: a larger mean alone does not imply more variability. If a calculator gives a statistical value, show the input list or summary statistic as required and write an interpretation sentence. For example, ‘Team A is more consistent because its standard deviation is smaller’ is stronger than merely listing two decimals.

One-minute retrieval: Variance and Standard Deviation

Close the worked solution. From memory, state its central rule, name one condition that makes it valid, and reconstruct one check that would catch a typical exam error.