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Algebra and geometry · Level 10

Statistics: grouped data

Mean, modal class and median class from grouped frequency tables.

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The idea

With grouped data, use the middle of each group as its value.

024681012141660–201020–401640–601260–80680–100families
024681012141660–201020–401640–601260–80680–100families

Look: Water used by 50 families. Most use 40–60 litres.

✏️ Your turn!

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  1. 1Middle of 25–35?

  2. 2Most common group above?

  3. 3How many families use under 40 litres?

! Careful!

  • ✗Using the group edges (0, 20…).

    ✓Use the middles (10, 30…).

  • ✗Dividing by the number of groups (5).

    ✓Divide by the number of families (50).

See the whole lesson on one page

With grouped data, use the middle of each group as its value.

Multiply each middle value by how many are in the group. Add them up. Divide by the total number. That gives the mean.

Think of it like thisIf 6 families use "20 to 40 litres", we guess each uses about 30 — the middle.

024681012141660–201020–401640–601260–80680–100families
024681012141660–201020–401640–601260–80680–100families
Water used by 50 families. Most use 40–60 litres.

Solved together

Question

Find the mean water use of these 50 families.

  1. Middles: 10, 30, 50, 70, 90. Multiply by the family counts.

    GroupFamiliesMiddleFamilies × middle0–206106020–40103030040–60165080060–80127084080–100690540
    GroupFamiliesMiddleFamilies× middle0–206106020–40103030040–60165080060–80127084080–100690540

  2. Add the last column.

    60 + 300 + 800 + 840 + 540 = 2,540

  3. Divide by 50 families.

    2,540 ÷ 50 = 50.8

AnswerMean 50.8 litres.

For older learners and grown-ups: a little more

Median for grouped data = l + [(n/2 − cf)/f] × h, where l is the lower edge of the median group, cf the running total before it, f its count and h its width. Here: 40 + (25 − 16)/16 × 20 = 51.25.

Now practise it

Kanakku makes new questions on statistics: grouped data every time. It shows the working and gives a hint when you are stuck.

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