When do mean and median differ most?

When extreme values pull the mean away from the middle of the data.

Why check where the axis starts?

If the axis does not start at zero, bar lengths stop showing true proportion.

Primary General Studies, Charts and Data, Paper 2: mean, median and choosing a chart

2026-10-31

Tutor Prep Guide · Primary General Studies

Ten items on a mean of 76.0, a median of 72, a mode of 3, a range of 27, averages of 3.0 against 2.5, 60 pet owners out of 200, slices adding to 100% and the trap of a cut axis.

Focus　The mean is the total over the count: 380 divided by 5 is 76.0; the median needs sorting first and gives 72; the mode is the most frequent value, 3; the range is 91 minus 64, or 27; with unequal group sizes compare per person: 96 over 32 is 3.0 against 70 over 28 at 2.5; 200 times 30% is 60; the slices add to 100% and 40% of 800 is 320; an axis starting at 90 exaggerates a real gap of just 2.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: Primary General Studies: Charts and Data
Level	P3 to P6

02　Questions (10 items)

FoundationFive quiz scores are 72 68 85 91 64. What is the mean?
FoundationWhat is the median of the same five scores 72 68 85 91 64?
FoundationWhat is the mode of 3 3 5 7 9?
FoundationWhat is the range of the same scores 72 68 85 91 64?
IntermediateClass 4A has 32 pupils borrowing 96 books; 4B has 28 pupils borrowing 70. Which class borrows more per pupil?
IntermediateIn a survey of 200 people, 30% keep pets at home. How many is that?
IntermediateA pie chart has four slices of 40% 25% 20% 15%. Do they add up correctly, and how many people does the largest slice stand for in a school of 800?
ChallengeWhen does the median describe a set of data better than the mean?
ChallengeA bar chart starts its vertical axis at 90, so bars of 98 and 100 look many times apart. What is the real difference and what is wrong with the chart?
Error redoA classmate says the mean of a data set must equal one of the values. Is that correct?

03　Answers and one-line notes

#	Answer	One-line note
1	The total 380 divided by 5 gives a mean of 76.0.	The mean is the total divided by the count, not the middle value.
2	In order they are 64 68 72 85 91, so the middle value is 72.	Sorting first is unavoidable when finding the median.
3	The mode is 3 because it appears most often.	The mode is about how often a value appears, not how large it is.
4	The largest 91 minus the smallest 64 gives a range of 27.	The range only uses the largest and smallest values.
5	4A is 96 divided by 32 at 3.0 books, and 4B is 70 divided by 28 at 2.5, so 4A borrows more.	With different group sizes, compare averages rather than totals.
6	200 times 30% gives 60 people.	Multiply the total by the percentage, then check the answer is a whole number.
7	The slices add to 100%, and the largest is 40%, which is 320 people out of 800.	Checking that the slices add to 100% is the quickest sanity test.
8	When there are extreme values: if most pupils score 70 but one scores 5, the mean is dragged down while the median still shows the typical score.	Extreme values are the signal to use the median.
9	The real difference is only 2. Starting the axis at 90 exaggerates the gap and misleads readers.	If the axis does not start at zero, bar length no longer shows proportion.
10	No. A mean can fall between the values, such as 2.5 for the numbers 2 and 3, and it need not equal the mode either.	Mean, median and mode are three different averages and must not be swapped.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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