Here are the maths-quiz scores for five people in a group: 3, 5, 7, 7 and 8.
If somebody asked you "how did that group do?" and you could only give them one number to describe the whole group, what number would you pick? Would you pick the biggest? The middle one? Something in between?
Take three hands-up answers, not open call-outs. Don't judge any answer yet — collect a spread. Listen for pupils reaching for "the average", "the middle", or "the most common"; those three are the mean, median and mode you are about to name.
Do not resolve it here — the point is to make pupils feel that one number is a choice, not an automatic thing.
Here are three dot plots. Every dot is one person's score, sitting above its value on the line. Watch how the mean and median lines sit in each picture, sometimes together and sometimes a little apart.
First plot 3, 5, 7, 7, 8: point at and name each measure — mean 6, median 7, mode 7, range 5. Mean and median differ by one here; that is just this set's shape, not an outlier, so don't over-explain — the outlier comes later.
Second plot 2, 4, 6, 8, 10: ask why no mode column is highlighted before revealing it — nothing repeats.
Third plot 1, 1, 2, 2, 9: the make-or-break set. Ask pupils to predict where the mean line will sit first. Then show 1 + 1 + 2 + 2 + 9 = 15, and 15 shared by 5 = 3. The 9 holds the mean out at 3 while the median stays at 2.
This set has two modes (1 and 2 both appear twice), which is why the mode overlay is off — mention two modes at once is normal but keep focus on the outlier.
Hold out for pupils naming the gap between the mean and median lines in the last picture — that gap is the whole lesson.
If any overlay fails to render: hand-draw the dots on a number line and mark mean, median, mode column and range bracket yourself so each measure is still seen in place.
Today we work through these sets together, in this order: 4, 6, 6, 8, then 5, 5, 5, 5, 5, then 2, 3, 3, 4, 8.
For each one we will line the dots up on the plot, then find the mean, the median, the mode and the range. The last set has a high value at the end, so we will look once more at where the mean and the median land, and predict which one is further out.
Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.
The plot carries one set at a time, so after each set clear the plot and drag in the next one. Build 4, 6, 6, 8 first, then clear and build 5, 5, 5, 5, 5, then clear and build 2, 3, 3, 4, 8.
For 4, 6, 6, 8 the mean is 6 and the median is 6 — a nice matched case. This is an even-count set, so there are two middle numbers: both are 6, so the median is exactly 6. Point out that when the two middle numbers are different you add them and share by two. For 5, 5, 5, 5, 5 ask what the range is before you reveal it (0 — every value the same). For 2, 3, 3, 4, 8 ask the class to predict whether the mean or the median lands further out once the 8 is in; then read them off (mean 4, median 3).
Watch for the classic slip: finding the median without first putting the numbers in order.
In your maths copy, work out all four statistics for this data set. Label each one so you have a clear four-line summary:
Here is the set — the number of books each person read this month: 2, 3, 3, 4, 8.
Remember to line the numbers up in order before you pick out the median.
Walk the room glancing for two things: numbers ordered before the median is chosen, and the range worked as biggest minus smallest. This is whole-class copybook practice, not marking — no individual grading.
Now we take turns at the board. For each set, work out the measure named, then use Check to confirm it before we move on.
We work these in order. First, find the median of 3, 5, 8. Next, find the mean of 4, 4, 7, 9. Then find the range of 2, 6, 6, 11. After that, find the mode of 5, 7, 7, 7, 9. Last, find the mean of the goals scored by the class team over four matches: 1, 2, 2, 15. Watch what the 15 does to that average.
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
On the final set, 1, 2, 2, 15, pause before Check: the median is only 2 but the mean is 5. Ask why the average ended up bigger than three of the four scores. That single high value — the 15-goal match — is what does it.
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