Two groups have an average of six. Does that mean their results look alike? A short classroom example can show why a correct average is useful but incomplete.
Build two groups of numbers
Write these fictional sets on paper: Group A contains 5, 6 and 7; Group B contains 1, 6 and 11. Each set totals 18, and each contains three numbers. Dividing 18 by three gives a mean of six in both cases.
Ask learners to calculate the totals before revealing the shared mean. Then place the numbers on a number line or represent them with counters. The two arrangements should look noticeably different even though the arithmetic average matches.
Describe the spread
Group A runs from five to seven, a range of two. Group B runs from one to eleven, a range of ten. The range is the largest value minus the smallest. It adds one piece of information about how spread out these small sets are.
Ask a practical question: if the numbers represented waiting times in minutes, would everyone in each group have had a similar experience? Keep the scenario clearly fictional. The point is to connect the calculation with the people or objects a dataset might describe.
Give the average a companion sentence
Have learners complete two statements: “Both groups have a mean of six” and “The individual values differ because…”. Encourage them to use the actual smallest and largest values rather than saying one group is simply better.
A range also leaves information out, especially in a larger dataset. It does not describe how all the values are distributed between the extremes. Here it is a first comparison, not a complete statistical analysis.
Finish by asking learners to invent another three-number set with a mean of six. Checking both the total and the spread turns an average from a final answer into the beginning of a better description.