Secondary 3 G2 Mathematics Tutor Bukit Timah | Cumulative Frequency and Median Estimation. Did you know? A cumulative-frequency curve can show where the middle observation lies without listing every value.
This Secondary 3 G2 Mathematics guide for Bukit Timah learners explains cumulative frequency and median estimation using worked examples, interpretation checks and independent practice. Follow the student’s current school chapter sequence.
What cumulative means
Cumulative frequency is the running total of frequencies up to a boundary. Frequencies 3, 5 and 2 become cumulative totals 3, 8 and 10.
Explain the relationship in words before using a formula. Then change one number and check whether the same method still works. The aim is independent reasoning rather than memorising one example.
Worked grouped data
Suppose intervals 0–10, 10–20 and 20–30 have frequencies 3, 5 and 2. Total frequency is 10; cumulative totals at the upper boundaries are 3, 8 and 10.
Explain the relationship in words before using a formula. Then change one number and check whether the same method still works. The aim is independent reasoning rather than memorising one example.
Plot the curve
Plot cumulative frequency against the upper class boundary, starting at the lower boundary with zero. Join plotted points smoothly or as instructed by the school.
Explain the relationship in words before using a formula. Then change one number and check whether the same method still works. The aim is independent reasoning rather than memorising one example.
Median estimate
With ten observations, locate cumulative frequency 5 (half the total) and read across to the curve. Linear interpolation within the 10–20 class gives 10+(5−3)/5×10=14 as an estimate.
Explain the relationship in words before using a formula. Then change one number and check whether the same method still works. The aim is independent reasoning rather than memorising one example.
Quartile estimates
The lower and upper quartiles correspond approximately to cumulative counts N/4 and 3N/4 on the graph. Read the associated horizontal values.
Explain the relationship in words before using a formula. Then change one number and check whether the same method still works. The aim is independent reasoning rather than memorising one example.
What the graph cannot tell
Grouped data do not reveal the exact original observations. Graph readings and interpolation are estimates, not exact recovered medians.
Explain the relationship in words before using a formula. Then change one number and check whether the same method still works. The aim is independent reasoning rather than memorising one example.
Check
The final cumulative frequency must equal total sample size, and the curve must not decrease as the measurement increases.
Explain the relationship in words before using a formula. Then change one number and check whether the same method still works. The aim is independent reasoning rather than memorising one example.
A seven-day revision routine
Day 1: identify the key quantities and units. Day 2: practise the first worked example. Day 3: vary one condition. Day 4: solve a question without the topic label. Day 5: correct the first mistaken step. Day 6: combine this skill with another Mathematics topic. Day 7: retest independently after a delay.
Frequently asked questions
What should I do first? Identify what is known, what is required and which conditions stay fixed. How do I check an answer? Substitute it into the original information, check units and test whether its magnitude makes sense. Why can the final number be wrong despite correct arithmetic? The equation or model may represent the wrong quantity.
Official syllabus and local tutorial context
Check the 2027 SEC G2 Mathematics K210 syllabus for the relevant topic and examination conditions. The unchanged eduKateSG Mathematics tutorial reference describes three-pupil small-group learning near Sixth Avenue. Confirm current Secondary 3 G2 availability, teacher, fees and timetable directly.
Related Secondary 3 G2 Mathematics guides
Continue with Reverse Percentages and Original Prices, Frequency Tables and Estimated Mean or Linear Graph Intersections.