Good Learning Co.
SavannahYear 8
← Maths
MathsProbability and data30 min★★★ difficulty

Comparing distributions: average and spread

Comparing two sets of data always needs two things: a typical value and how spread out the data is. One without the other tells half a story.

Lesson overview

What you'll learn in this lesson

Describe, interpret and compare observed distributions of a single variable through appropriate measures of central tendency and spread

Key learning points

  • • Three averages, three jobs
  • • When the mean misleads
  • • Spread matters
  • • Writing a comparison

This lesson at a glance

  • 30 minutes
  • 19 parts to scroll through
  • 4 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

interpretobserveddistributionssinglevariable

Scroll down — the lesson carries on below

Part 1 of 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Comparing distributions: average and spread

An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.

In a nutshell

Describe, interpret and compare observed distributions of a single variable through appropriate measures of central tendency and spread

2

What you already know

Part 2 of 19

Before we start

What you already know

You can find the mean, median, mode and range of a small data set.

Recap: Rounding, estimating and checking
3

Key words

Part 3 of 19

Key words

Words you'll need today

median
The middle value when the data is in order.
range
The largest value minus the smallest — a measure of spread.
outlier
A value far away from the rest of the data.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Part 1 — Choosing an average

A short piece of teaching, then a check to make sure it has landed.

5

Explore the idea

Part 5 of 19

Learn

Three averages, three jobs

The mean uses every value, so it is affected by outliers. The median is the middle value and ignores extremes, which makes it the right choice for house prices or salaries. The mode is the most common value and is the only average that works for categories like favourite colour.

6

Explore the idea

Part 6 of 19

Learn

When the mean misleads

For 4, 5, 5, 6, 80 the mean is 20 — higher than all but one value. The median, 5, describes the data far better. Whenever you see a value far from the others, say so and use the median. Being able to justify your choice is worth as much as the calculation.

7

Quick check

Part 7 of 19

Quick check

Median of 3, 9, 4, 7, 5?

8

Quick check

Part 8 of 19

Quick check

Which average is most affected by an outlier?

9

Reset break

Part 9 of 19

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
10

Learning cycle

Part 10 of 19

Learning cycle 2 of 2

Part 2 — Comparing fairly

A short piece of teaching, then a check to make sure it has landed.

11

Explore the idea

Part 11 of 19

Learn

Spread matters

Two classes both average 62% in a test, but one has a range of 10 and the other 55. Same typical mark, completely different classes: one is consistent, the other has some very high and very low scores. Range is easily distorted by a single outlier, so mention it when quoting one.

12

Explore the idea

Part 12 of 19

Learn

Writing a comparison

A full comparison has two sentences, both in context. 'The mean mark for class A (68%) was higher than for class B (61%), so class A did better on average. Class A's range (12) was smaller, so their marks were more consistent.' Numbers plus meaning — that is what the marks are for.

13

Quick check

Part 13 of 19

Quick check

Range of 12, 4, 19, 7?

14

Quick check

Part 14 of 19

Quick check

Two sets have equal means but different ranges. This shows different...

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Forgetting to put the data in order before finding the median.
  • Comparing only averages and never spread.
  • Quoting numbers with no sentence explaining what they show.
16

Challenge round

Part 16 of 19

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

17

Challenge round

Part 17 of 19

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Range is easily distorted by a ____ outlier, so mention it when quoting one.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Comparing distributions: average and spread

6 questions, marked with the reasoning shown. No timer.

  1. 1. Best average for house prices?

  2. 2. Mean of 6, 8, 11, 15?

  3. 3. Only average usable for favourite colour?

  4. 4. A smaller range means the data is more...

  5. 5. Median of 2, 4, 6, 10?

  6. 6. A good comparison includes...

19

Lesson round-up

Part 19 of 19

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 19 · Watch & discover

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