Secondary 3 G2 Mathematics Tutor Bukit Timah | Frequency Tables and Estimated Mean. Did you know? A grouped-data mean is an estimate, not a recovered list of original observations.
This quick-reference guide explains frequency tables and estimated mean for Secondary 3 G2 Mathematics students in Bukit Timah, with worked examples, mistakes to avoid and independent practice.
Why frequency matters
A frequency table records how often each value or interval occurs. For exact values 2, 3, 4 with frequencies 1, 2, 1, the mean is (2×1+3×2+4×1)/4=3.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Grouped intervals
Suppose times fall into 0 to under 10 minutes (frequency 2), 10 to under 20 (frequency 3) and 20 to under 30 (frequency 1). The class midpoints are 5, 15 and 25.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Estimated mean
Multiply each midpoint by its frequency: 5×2+15×3+25×1=80. Total frequency is 6, so estimated mean = 80/6 ≈ 13.3 minutes.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Why estimated?
The original observations within each interval are unknown. The midpoint method assumes a representative value for each class and therefore may differ from the actual mean.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Frequency check
The total frequency must equal the number of observations. If 2+3+1=6 but a student divides by three classes, the mean is wrong.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Self-check
For midpoints 10 and 20 with frequencies 3 and 1, estimated mean = (30+20)/4=12.5. It should lie between 10 and 20.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Frequently asked questions
What should I do first? Identify the given values and the quantity required. How can I check the result? Substitute it into the original information and verify the units or graph. Why might a correct-looking answer fail? A sign, denominator or interpretation error can change the meaning of the result.
Official syllabus and tutorial context
Consult the 2027 SEC G2 Mathematics K210 syllabus for the official topic and assessment scope. The unchanged eduKateSG three-pupil Mathematics reference describes small-group teaching near Sixth Avenue. Confirm current Secondary 3 G2 tutor, fees, venue, group fit and timetable directly.
Continue the Secondary 3 G2 Bukit Timah series
For further Mathematics revision, see factorisation by grouping, quadratic graphs, and critical reading of data.