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Year 8 Maths | Understand, justify, check

Choose a summary that represents the data

A summary measure answers a particular question about data. The mean shares the total equally; the median identifies a middle position. An unusual observation can affect these summaries differently, so selecting a measure requires context.

What to notice

The median depends on ordered values, not the order in which measurements were recorded. The mean uses every observation, including unusually large or small values.

What to do

Write the dataset in order, count the observations and decide which summary is requested. Calculate with units, then compare the summary with the original spread of values.

Why it works

Looking back at the data helps prevent a correct number from becoming a misleading description. A mean may be pulled away from the cluster of typical values by an outlier.

Work through an example

Compare the mean and median of 4, 5, 5, 6 and 20 minutes.

  1. The ordered middle value is 5, so the median is 5 minutes.
  2. The total is 40; dividing by 5 gives a mean of 8 minutes.
  3. The 20-minute observation raises the mean above the four smaller values.

A common mistake

Do not remove an unusual observation merely because it changes the answer. First investigate whether it is a valid measurement and explain any decision to exclude it.

A strategy to try

Ask what the summary conceals. Two datasets can share a mean while having different spreads, and neither the mean nor median describes every observation.

Try it now

Try three questions

No account is needed. These examples do not change saved learning progress. Choose an answer and check it for an explanation; you can try again.

1. The chart shows 4, 6 and 8 laps in three sessions. What is the mean?
0A4B6C8
Three sessions: A 4 laps, B 6 laps, C 8 laps. Bars begin at zero.
Help: a starting point

Find the total laps across all three sessions.

Help: the next step

Share the total equally among the number of sessions.

2. What is the median of 9, 2, 7, 4 and 3?
Help: a starting point

Put the five observations in increasing order.

Help: the next step

With an odd number of observations, locate the single middle position.

3. In 4, 5, 5, 6, 20, the value 20 changes to 40. Which statement is correct?
Help: a starting point

Compare the old and new totals while keeping the number of observations fixed.

Help: the next step

Then check whether the middle ordered value has changed.

For parents and carers

Discuss which value sounds typical and why before checking the calculation. The final question is about the effect of an outlier, not a rule that one measure is always better. Small practice datasets are chosen for clarity, not as evidence about a real population.

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