Averages, range and honest charts
Two datasets can share a mean and tell completely different stories. The range, and the shape of the chart, is where the truth lives.
Part of your national curriculum
- Statistics: Describe, interpret and compare observed distributions of a single variable through appropriate measures of central tendency and spread
- Statistics: Construct and interpret appropriate tables, charts and diagrams, including bar charts, pie charts and pictograms for categorical data, and vertical line charts for ungrouped discrete numerical data
Lesson overview
What you'll learn in this lesson
Compare distributions using the mean and range
Key learning points
- • Mean, median, mode, range
- • Charts that mislead
This lesson at a glance
- 30 minutes
- 10 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 10
Watch first
Averages, range and honest charts
An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.
In a nutshell
Compare distributions using the mean and range
Explore the idea
Part 2 of 10
Learn
Mean, median, mode, range
The mean is pulled by extremes; the median is not. Range measures spread. Quote a measure of centre with a measure of spread or you have said very little.
Explore the idea
Part 3 of 10
Learn
Charts that mislead
A vertical axis that does not start at zero exaggerates differences. Always read the axis before the bars.
Quick check
Part 4 of 10
Quick check
Which average is least affected by one huge value?
Quick check
Part 5 of 10
Quick check
Range measures…
Quick check
Part 6 of 10
Quick check
A truncated y-axis tends to…
Challenge round
Part 7 of 10
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
Challenge round
Part 8 of 10
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
The mean is pulled by extremes; the ____ is not.
Mastery quiz
Part 9 of 10
Marked quiz
End of lesson quiz: Averages, range and honest charts
3 questions, marked with the reasoning shown. No timer.
1. Which average is least affected by one huge value?
2. Range measures…
3. A truncated y-axis tends to…
Lesson round-up
Part 10 of 10
Lesson round-up
Ready when you are
Quiz score
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Games
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Points this lesson
0
Best run
0 in a row
Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaDo 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.
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
- Work out the total cost of the trip if 50 pupils go.
- Show why the price per pupil falls when more pupils go, using numbers.
- At £20 each, how many pupils must go before the trip makes money? Show your working.
Working out
Working outDo 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
WritingCopy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working outWrite your own real-life problem that uses today's method, then solve it.
1 problem + solution
Saved as you type.
Part 1 of 10 · Watch & discover
How this is going
- Not looked at yet
Describe, interpret and compare observed distributions of a single variable through appropriate measures of central tendency and spread
- Not looked at yet
Construct and interpret appropriate tables, charts and diagrams, including bar charts, pie charts and pictograms for categorical data, and vertical line charts for ungrouped discrete numerical data