Ad Banner Placeholder

Cambridge IGCSE Mathematics — 0580 Extended

Topic 9.2: Statistics — Interpreting Data

Extended papers ask you to read a diagram, compare two sets, and refuse a conclusion the sample cannot support. Quote an average and a measure of spread together. Underline the group named in the sentence before you pick a total.

Read the diagram

Dual (side-by-side) bars compare the same category across two groups. Composite (stacked) bars show the split inside one group.

Dual bar chart of grades A to D for Class A and Class B
Class A has more A and B grades. Class B piles up at C.
Stacked bar chart of boys and girls in Years 10, 11 and 12
The stack total is the year size. Dual bars are easier if you must compare one colour.

Compare with average and spread

Two classes can share a mean and still look nothing like each other. The range (or IQR, later) is the second sentence of the comparison.

Both classes have mean 63. Which is more consistent?

Two number lines: Class A spread from 48 to 86, Class B tightly around 63
Means match. Class B’s range is 10; Class A’s is 38. Class B is more consistent.

The denominator is the named group

18 Year 10s come by bus. That is 18 out of the 30 Year 10s, not 18 out of all 60 students — unless the question says “of all students”.

Method

  1. Underline the group: “of the Year 10s”, “of those who walk”, “of all 60”.
  2. That total is the denominator.
  3. The cell (or bar height) is the numerator.
Two-way table of year group against bus or walk, with 18 of 30 highlighted
18/30 = 3/5 of Year 10s. 18/60 = 3/10 of everyone. Different questions.

Restrictions on conclusions

E9.2 asks you to appreciate what the data cannot prove. A comment, not another calculation.

Four caveats: small sample, sample bias, correlation is not causation, missing spread
Eight students do not speak for 120. A mean without a range can hide 20% and 100%.

Paper 2 (non-calculator)

\(18/30 = 3/5\) by cancelling 6. \(18/60 = 3/10\). The two fractions are not interchangeable.

Try this

From the journey table, what fraction of Year 11 students walk?

Show answer
Answer

  1. Year 11 row, Walk column 20; Year 11 total 30.

    \[ \dfrac{20}{30} = \dfrac{2}{3} \]

Exam Traps

  • Dividing by the grand total when the question said “of the Year 10s” (or “of those who take the bus”) is the mark lost on almost every two-way reading.

0/10

Ad Banner Placeholder