Taught through the hedgehog weight records
Approx. 50 minutes · KS3
Before you start
Every hedgehog here is weighed regularly and the number written down. That record is the single most useful health tool a keeper has, because an animal that is losing weight is telling you something several weeks before it looks unwell.
This lesson uses real-shaped weight data to teach the statistics you need at KS3.
Nothing here is timed or scored.
What you'll be able to do by the end
- Calculate the mean, median, mode and range of a set of data.
- Choose which average suits a situation and explain why.
- Read and construct a frequency table.
- Draw and interpret a line graph showing change over time.
- Spot what a graph is hiding as well as what it shows.
Part 1 — The four numbers
Here are the weights, in grams, of nine adult hedgehogs on one weighing day:
412, 385, 460, 402, 385, 521, 398, 430, 385
Mode — the most common value.
385 appears three times. Mode = 385 g
Median — the middle value once ordered.
Ordered: 385, 385, 385, 398, 402, 412, 430, 460, 521
Nine values, so the fifth is the middle. Median = 402 g
Mean — the total divided by how many.
Total = 3778. 3778 ÷ 9 = 419.8 g (1 d.p.)
Range — the spread, largest minus smallest.
521 − 385 = 136 g
The step people skip
Order the data before finding the median. Every single time. Finding "the middle one" in an unordered list is the most common error in this topic and it is entirely avoidable.
Part 2 — Which average, and why
They give three different answers from the same data. That is not a problem with maths; it is the point. Each one tells you something different.
The mean, 419.8 g, uses every value — but that 521 g hedgehog pulls it upward. Remove her and the mean drops to 407 g. A single unusual value, an outlier, can drag the mean somewhere unrepresentative.
The median, 402 g, ignores how extreme the extremes are. The 521 g animal counts as one value, no more. This makes it more reliable when there are outliers.
The mode, 385 g, is the only one that must be a real value from the data. Useful when you want a typical case rather than a calculated one, and the only average available for non-numerical data — you cannot take the mean of a list of species.
Check yourself
A keeper wants a figure to describe "a typical hedgehog weight here" for a care guide. Which average would you recommend, and why?
Model answer
The median, at 402 g. The data contains an outlier at 521 g which pulls the mean above what most of the animals actually weigh, so the mean would overstate a typical weight. The mode of 385 g is the lowest cluster and would understate it. The median sits in the middle of the actual distribution and is not distorted by the extreme value.
Part 3 — Frequency tables
With nine animals you can list every weight. With sixty you cannot, so you group them.
| Weight, w (g) | Frequency |
|---|---|
| 350 ≤ w < 400 | 4 |
| 400 ≤ w < 450 | 3 |
| 450 ≤ w < 500 | 1 |
| 500 ≤ w < 550 | 1 |
Check the total: 4 + 3 + 1 + 1 = 9. Always check.
Reading the notation. 350 ≤ w < 400 means 350 or more, but under 400. A hedgehog weighing exactly 400 g goes in the next row. This matters — groups must not overlap, or a value could go in two places.
Check yourself
Which group would a 450 g hedgehog go in, and why?
Answer
The 450 ≤ w < 500 group. The symbol ≤ means "less than or equal to," so 450 is included in that group's lower boundary. It is excluded from the previous group because that one requires w < 450, which 450 is not.
Part 4 — Graphs over time
One hoglet, weighed weekly:
| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Mass (g) | 18 | 34 | 55 | 78 | 96 | 108 | 114 | 117 |
Plotted as a line graph, this curve rises steeply then flattens. That shape is the whole story:
- Weeks 1–4: rapid growth. Steep gradient. The mass roughly doubles, then doubles again.
- Weeks 5–8: growth slowing. The line flattens as the animal approaches adult size.
A flattening line does not mean something is wrong. It means the rate of growth is falling, which is exactly what should happen. What would be a concern is the line turning downward.
Reading a graph properly
Three questions, every time:
- What are the axes? Including the units. A graph in kilograms looks identical to one in grams.
- Does the vertical axis start at zero? If it does not, differences look far larger than they are. This is the most common way a graph misleads honestly.
- What is not shown? Eight weeks of one animal is not the same as eight weeks of every animal.
Check yourself
Between which two consecutive weeks was the growth greatest, and by how much?
Answer
Weeks 2 to 3, a gain of 21 g.
Check the others: 16, 21, 23, 18, 12, 6, 3 — so in fact weeks 3 to 4 is the largest at 23 g.
If you answered 2 to 3, you found a big gap but not the biggest. Work out every difference before deciding — this is exactly why the check matters.
Part 5 — Questions
1. Find the mean, median, mode and range of: 220, 245, 220, 260, 235, 255, 220. (4 marks)
Answer
Ordered: 220, 220, 220, 235, 245, 255, 260
Mode = 220
Median = 235
Mean = 1655 ÷ 7 = 236.4 (1 d.p.)
Range = 260 − 220 = 40
2. A set of six weights has a mean of 400 g. Five of them are 380, 395, 410, 405 and 390. Find the sixth. (3 marks)
Answer
Total needed = 400 × 6 = 2400 (1)
Sum of the five given = 1980 (1)
Sixth weight = 2400 − 1980 = 420 g (1)
3. Explain one situation where the median is a better average than the mean. (2 marks)
Answer
When the data contains an outlier or extreme value (1), because the mean is pulled towards it and would misrepresent a typical value, whereas the median is not affected by how extreme the extremes are (1).4. A graph of animal weights has a vertical axis starting at 380 g rather than 0. Explain how this could mislead someone reading it. (2 marks)
Answer
Differences between the bars or points appear much larger than they actually are (1), because only a narrow slice of the range is shown, so a small real difference fills a large part of the graph (1).If you want to go further
- Weigh something at home once a week for eight weeks and graph it. A pet, a plant, a loaf of bread going stale — the method is identical.
- Related lessons: Probability · Percentages · GCSE Maths — Ratio, Proportion & Rates of Change.
Notes for the adult
Curriculum: KS3 Maths — mean, median, mode and range; grouped frequency tables; constructing and interpreting graphs; and the effect of outliers on measures of average.
The misconception this lesson targets: that "average" means the mean, always. Part 2 is built to show three defensible answers from one dataset.
A deliberate trap. The final self-check in Part 4 is designed so a plausible answer is wrong. The answer names the mistake rather than just correcting it, because a student who has just made it needs to see why. If that would knock a fragile learner's confidence, do that question together.
Access: read-aloud, dyslexia-friendly font, enlarged text, high contrast and calm mode. Tables are simple two- and three-column layouts that read sensibly with read-aloud enabled, and print cleanly.
No timing, no scoring.
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