Good Learning Co.
SavannahYear 8
← Maths
MathsAnimal data handling30 min★★★ difficulty

Averages and spread: comparing two populations fairly

Two groups of animals can have the same mean mass and be nothing alike. Spread is where the real story usually is.

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 uses
  • • Outliers deserve a decision, not deletion
  • • Spread completes the picture
  • • Writing a fair comparison

This lesson at a glance

  • 30 minutes
  • 18 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 18 · Discover6%
1

Watch & discover

Part 1 of 18

Watch first

Averages and spread: comparing two populations fairly

An English teaching video on this topic from Cardiff High School KS3 Maths. 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 18

Before we start

What you already know

You should already know how to calculate the mean, median, mode and range of a set of values.

3

Key words

Part 3 of 18

Key words

Words you'll need today

Mean
Total divided by the number of values.
Median
The middle value when data is in order.
Mode
The most common value.
Range
Largest value minus smallest value.
Outlier
A value far from the rest of the data.
4

Learning cycle

Part 4 of 18

Learning cycle 1 of 2

Which average, and why

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

5

Explore the idea

Part 5 of 18

Learn

Three averages, three uses

The mean uses every value, so it is sensitive to outliers. The median ignores extremes, which makes it better for skewed data such as territory sizes. The mode is the only average available for categorical data, such as the most commonly recorded species.

6

Explore the idea

Part 6 of 18

Learn

Outliers deserve a decision, not deletion

One 90 kilogram individual in a sample of 20 kilogram animals may be a recording error, a different species, or a genuinely exceptional animal. Investigate first; if you exclude it, say so and say why. Quietly deleting inconvenient data is not statistics.

7

Quick check

Part 7 of 18

Quick check

Which average is least affected by an outlier?

8

Reset break

Part 8 of 18

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
9

Quick check

Part 9 of 18

Quick check

Site A: 11–13 birds. Site B: 2–25 birds. Both mean 12. Which is steadier?

10

Learning cycle

Part 10 of 18

Learning cycle 2 of 2

Comparing with spread

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

11

Explore the idea

Part 11 of 18

Learn

Spread completes the picture

Two feeding sites might both average 12 birds per hour, but one ranges 11 to 13 and the other 2 to 25. Same mean, entirely different reliability. The range is quick; comparing the middle of each distribution, using the median with the highest and lowest values, is more robust.

12

Explore the idea

Part 12 of 18

Learn

Writing a fair comparison

A strong comparison names the measure, quotes numbers and interprets: "the reserve had a higher median count (14 against 9) and a smaller range (6 against 17), so counts there were both larger and steadier." That sentence is the mathematics doing work.

13

Quick check

Part 13 of 18

Quick check

For 'most commonly recorded species' the appropriate measure is the

14

Quick check

Part 14 of 18

Quick check

A single 90 kg reading among 20 kg animals should first be

15

Common mix-ups

Part 15 of 18

Common mix-ups

Things people often get wrong

  • The mean is not always the best average; skewed data suits the median.
  • A large range does not mean the mean is wrong, only that values vary widely.
  • Outliers should be investigated, not automatically removed.
16

Challenge round

Part 16 of 18

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

Mastery quiz

Part 17 of 18

Marked quiz

End of lesson quiz: Averages and spread: comparing two populations fairly

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

  1. 1. Range is calculated as

  2. 2. The mean of 4, 6, 6, 12 is

  3. 3. The median of 3, 5, 9, 11 is

  4. 4. Skewed data is better summarised by the

  5. 5. A fair comparison of two sites should include

  6. 6. If you exclude an outlier you must

18

Lesson round-up

Part 18 of 18

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 18 · Watch & discover

Good Learning Co. — personalised UK curriculum learning, built around what each learner loves.