Did you know? A set of seven numbers can have a mean of 7, a median of 6 and a mode of 5—all at the same time. None of those calculations is automatically wrong. They are answering three different questions about the same data.
Quick answer: For Secondary 4 G1 Mathematics students in Bukit Timah, learn to calculate the mean, median and mode for ungrouped data, then explain which measure is most informative for the question. The 2027 SEC Mathematics K110 syllabus explicitly includes the purposes and uses of these averages. It is not enough to memorise three definitions.
The same data, three different stories
Imagine these invented daily practice times, in minutes, for seven sessions: 3, 5, 5, 6, 8, 9, 13. The numbers are already in ascending order, which makes our median easier to identify.
The mean is the sum divided by the number of observations: (3 + 5 + 5 + 6 + 8 + 9 + 13) ÷ 7 = 49 ÷ 7 = 7 minutes. Every data value contributes to it.
The median is the middle number after sorting. There are seven observations, so the fourth is in the middle. The median is 6 minutes.
The mode is the value that occurs most often. Five appears twice, while each other number appears once. The mode is 5 minutes.
Which one is the ‘average’? In everyday speech, people may use ‘average’ loosely. In Mathematics, it helps to name the measure. The mean describes a balance point of all recorded values, the median divides ordered observations in half, and the mode identifies the most frequent observation.
Now change one value—watch the mean move
Suppose the longest session was not 13 minutes but 51 minutes. The revised data are 3, 5, 5, 6, 8, 9, 51. Their sum is now 87, so the mean becomes 87 ÷ 7 ≈ 12.4 minutes to three significant figures.
What about the median? The fourth number is still 6. The mode is still 5. One unusually large observation has moved the mean sharply, but has not moved the middle value or most frequent value.
If a parent asks what a typical session looks like, the median might now tell a clearer story than the mean. If the question asks for the total time spent across all sessions, however, the mean still connects directly to the total. We choose the statistic for a purpose, not because one measure is universally better.
Example 2: the median when there are an even number of values
Consider four scores: 10, 12, 14, 20. There is no single middle observation. The two middle values are 12 and 14, so the median is (12 + 14)/2 = 13.
The mean is (10 + 12 + 14 + 20)/4 = 14. In this dataset, each score appears only once, so there is no mode. It would be incorrect to invent a most frequent value simply because the question asks you to find one.
A frequent student mistake is to choose the second number as the median for any list of four. The correct rule is to average the two middle numbers after ordering the data.
Example 3: mean from a simple frequency table
Suppose a small survey records an ungrouped numerical value of 2 on three occasions, 4 on two occasions and 7 on one occasion. The frequency table tells us there are 3 + 2 + 1 = 6 observations in total.
Add the observations using frequency: 2 × 3 + 4 × 2 + 7 × 1 = 21. The mean is 21/6 = 3.5. The ordered list is 2, 2, 2, 4, 4, 7, so the median is (2 + 4)/2 = 3, and the mode is 2.
This is an ungrouped frequency table, not a table of measurement intervals. If only broad intervals such as 0–10 or 10–20 are known, we cannot generally recover every exact observation without more information. Do not present a midpoint-based estimate as if it were the exact original mean.
Where range and interquartile range fit
Averages tell us about the centre or typical value. They do not tell us how scattered the observations are. For the original dataset 3, 5, 5, 6, 8, 9, 13, the range is 13 − 3 = 10.
Using the common school method that excludes the median when the dataset has an odd number of values, the lower half is 3, 5, 5 and the upper half is 8, 9, 13. Thus Q1 = 5, Q3 = 9 and the interquartile range is 9 − 5 = 4.
This makes the interpretation richer: the mean is 7, but the central half of the data occupies a narrower interval than the full range. Always follow the method and definition specified by your school or examination question where different quartile conventions are relevant.
A fast decision guide: mean, median or mode?
- Mean: useful when the problem involves a numerical total or we want every value to contribute to a summary.
- Median: useful for describing the middle of ordered data, especially when an unusually extreme value would distort the mean.
- Mode: useful for identifying the most commonly occurring value or category. A dataset may have more than one mode—or none.
- Range and interquartile range: useful when the question is about spread rather than just centre.
What the official G1 K110 syllabus says
The 2027 SEAB G1 Mathematics K110 syllabus includes the purpose and use of mean, mode and median; their calculation for ungrouped data; and percentiles, quartiles, range and interquartile range. These belong to the Statistics and Probability strand, which the published 2027 scheme places in Paper 2 along with Number and Algebra.
The SEAB 2027 G1 school-candidate subject list gives Mathematics code K110, with code 4046 shown for reference to 2026 and earlier. This article discusses 2027 syllabus content; students taking an examination in 2026 should refer to their own registered subject-level exam details.
Try a five-minute home check
Give the data 2, 4, 4, 6, 9. The mean is (2 + 4 + 4 + 6 + 9)/5 = 5. The median is 4 and the mode is 4. Then replace the 9 with 29. The mean becomes 9, but the median and mode stay at 4.
Ask your child which value gives a better impression of the four more usual observations. Listen for a reason. The point of data analysis is to explain what a number tells us, not just produce a neat calculation.
What a Secondary 4 G1 Mathematics tutor should inspect
Look for the first mistaken step: was the data not ordered, was one observation omitted, were frequencies ignored, or did the student confuse a mode with a median? It helps to teach the correct calculation and then ask the learner to explain what it means in one short sentence.
The unchanged eduKateSG Clementi small-group teaching reference describes a feedback-led three-student approach for a separate Secondary 1 Maths class. Contact the provider directly to confirm current Secondary 4 G1 arrangements; the reference does not establish a timetable or seat availability.
Frequently asked questions
Can the mean be a number that never appears in the data? Yes. The mean is a calculated balance point, not necessarily one of the recorded values.
Can a set have two modes? Yes. Two values can tie for the highest frequency.
Why does the median sometimes work better with an outlier? It depends on order rather than the exact size of the extreme value, so a very large or small observation may have less effect on the median.
Continue exploring data and probability
Read quartiles, data and probability, histograms and cumulative frequency, and single-event probability.