The mean, median and mode each answer a different question, so the skill is to read the question first and choose the average second. Choosing appears in short context questions throughout statistics and distributions, often with a mark for the reason.
What does each average actually tell you?
- Mean: the total shared out equally. It uses every value, so it reacts to extremes.
- Median: the middle value when the data is in order. It ignores how extreme the ends are.
- Mode: the most frequent value or category. It needs no arithmetic and works for categories such as colours or sizes.
A useful test is to ask “what is the question really asking for?”. A fair share of a total points to the mean.
The middle of the group points to the median. The most popular choice points to the mode.
How to choose, step by step
- Read the wording and underline the thing being asked: typical, fair share, most common.
- Scan the data for values far from the rest. Sort the data if that helps.
- Pick the average that matches the wording and is not distorted by the data.
- Calculate it, showing the sort order for a median and the total for a mean.
- State the reason in one short sentence.
Worked example
Five staff at a small shop earn the following monthly pay (RM): 2400, 2500, 2600, 2700, 12400. The owner says, “Our typical pay is about RM4500.” Is that a fair description?
Step 1, mean: 2400 + 2500 + 2600 + 2700 + 12400 = 22600, and 22600 ÷ 5 = RM4520.
Step 2, median: the data is in order, and the middle of five values is the third, RM2600.
Step 3, compare with the data: four of the five staff earn RM2700 or less. A mean of RM4520 is higher than four out of five people.
Step 4, conclude: the median, RM2600, is the better description of typical pay, because the single value of RM12400 pulls the mean upward.
The mean is not wrong as a calculation. It answers a different question, which is “what would each person get if the total pay were shared equally?”.
The mistake to watch for
A common slip is to always use the mean because it feels more “mathematical”, then to call it typical.
Mistaken answer: “The typical pay is RM4520, because that is the mean.”
The mean is correct arithmetic, but the reason is missing and the conclusion does not fit the data.
The correction is to check for an extreme value before you commit. If one value sits far from the rest, say the median is more suitable and give that reason. If the question asks for a fair share of a total, the mean is right.
Check yourself
Try these without a calculator, then open each answer.
1. A shoe shop sold these sizes in one day: 5, 6, 6, 7, 7, 7, 8, 9. Which average helps the owner decide which size to order most of, and what is it?
Show answer
The question asks for the most common size, so use the mode. Size 7 appears three times, more than any other, so the mode is size 7.
2. Five runners take 14, 15, 15, 16 and 40 seconds. Find the mean and the median, then say which describes a typical runner.
Show answer
Mean: 14 + 15 + 15 + 16 + 40 = 100, and 100 ÷ 5 = 20 seconds. Median: the third value in order is 15 seconds.
Four of the five runners took 16 seconds or less, so the median describes a typical runner better. The 40 seconds pulls the mean up.
3. Five students scored 12, 15, 15, 18 and 20 on a quiz. The teacher wants to give every student the same score so that the class total stays unchanged. What score is that?
Show answer
Sharing a total equally is the mean. The total is 12 + 15 + 15 + 18 + 20 = 80, and 80 ÷ 5 = 16.
Where this leads next
Once choosing an average is routine, learn how to calculate a weighted mean, which is what you need when the values do not count equally. You can test your choices with the statistics and distribution explorer, and keep your arithmetic tidy with the non-calculator working trainer. The whole module is tested in the mixed practice set.
Some students calculate correctly but still lose the reasoning mark because the justification is vague. That is the sort of pattern our teachers look for in online one-to-one Mathematics tuition.