Statistics Problem Solving (11+ Style)

S10Statistics Problem Solving

Charts, averages and tables together.

Real data questions chain skills: read the chart, compute the average, check the claim.

Is Jay right? ‘The mean of my four scores is over 10.’ Scores: 9, 12, 8, 11.

9 + 12 + 8 + 11 = 40

40 ÷ 4 = 10

Mean = 10 — Jay is wrong (not OVER 10).

Data problems end with a decision — calculate, then answer the actual claim.

Learn the 4-Step Method

1Read the data carefully.

Chart scales, table totals, pictogram keys — collect the numbers first.

collect 📋

2Choose the right measure.

‘Typical’ → mean or median · ‘most common’ → mode · ‘spread’ → range.

which measure?

3Calculate and compare.

Work it out, then compare against the claim or the other data set.

compute → compare

4Answer the question asked.

Yes/no claims need the number AND the verdict: ‘mean = 10, so no’.

number + verdict

💡 Key Idea‘Show your working’ questions award marks for the calculation AND the conclusion — write both.

Worked Example

Team A's scores: 7, 9, 8. Team B's: 4, 12, 8. Which team is more consistent?

Range A

9 − 7 = 2

Range B

12 − 4 = 8

✓ Verdict

Team A — smaller range (2 vs 8) means more consistent.

Both means are 8 — the range decides!

Watch Out! Common Mistakes

Stopping at the calculation.

Finish the job! ‘Mean = 10’ doesn’t answer ‘is Jay right?’. Add the verdict: no — 10 is not over 10.

Mean when the question wants range.

Match the measure! ‘More consistent’ is about spread → use the range, not the mean.

Misreading the data source.

Back to basics! Most wrong answers start with a misread scale or key. Re-read the chart before trusting your numbers.

⬇ Cheat Sheet

STATISTICS PROBLEM SOLVING

Collect the numbers carefully (scales, keys, totals).
Match the measure to the question word.
Calculate, then compare.
Answer with the number AND the verdict.

Example: means equal → compare ranges: 2 vs 8 → Team A more consistent.

📖 Continue Your Journey

✓ S1 Tally Charts and Pictograms ✓ S2 Bar Charts ✓ S3 Line Graphs ✓ S4 Pie Charts ✓ S5 The Mean ✓ S6 Median, Mode and Range ✓ S7 Two-Way Tables ✓ S8 Venn and Carroll Diagrams ✓ S9 Probability Basics S10 Statistics Problem Solving

→

You’ve completed the Statistics Journey! 🎉Back to the Statistics Hub

📄 Free printable: Download the Statistics Problem Solving cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Collect the data first, watching scales and keys.
Match the measure to the question: typical → mean/median, most common → mode, consistent → range.
Calculate, compare, and state the verdict — not just the number.
Equal means? The range often decides the answer.

Frequently asked questions

How should children answer 'is this claim right?' questions?

Calculate the relevant measure, then explicitly compare it with the claim: 'The mean is 10, and 10 is not over 10, so the claim is wrong.' Both parts earn marks.

Which average should be used for 'more consistent'?

The range — consistency is about spread, and the smaller range wins. Means can be identical while ranges differ wildly.

What data skills matter most for the 11+?

Reading scales and keys accurately, the four measures (mean, median, mode, range), two-way tables and claim-checking — the exact chain practised in this series.

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