To compare the same percentile on two cumulative frequency graphs, use each group’s own total. For the 75th percentile, multiply each group size by 0.75, then read across from that cumulative frequency and down to the horizontal axis.
The 2027 SEC G3 Mathematics K310 syllabus covers cumulative frequency diagrams and percentiles. This guide shows how two curves can pass through the same cumulative frequency and still represent different shares of their groups.
- Find the total represented by each curve.
- Multiply each total by the percentile as a decimal.
- Read across to the curve and down to the data axis.
- Compare the two data values in the units shown.
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Start with the total for each curve
Suppose a graph shows journey times for Group A with 40 students and Group B with 60 students. Each curve finishes at its own total. A cumulative frequency of 30 means that 30 students are counted up to the corresponding journey time. That is three quarters of Group A but only half of Group B.
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Worked example | Find each upper quartile
For Group A, use 0.75 × 40 = 30 on the cumulative frequency axis. Suppose this meets curve A at about 24 minutes. For Group B, use 0.75 × 60 = 45. Suppose the corresponding reading is about 28 minutes. Group B has the higher upper quartile by about 4 minutes.
Reading both curves at 30 would compare Group A’s upper quartile with Group B’s median. The horizontal positions could be read accurately and still answer a different question.
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Reverse the direction when the question gives a time
Suppose 20 minutes corresponds to cumulative frequencies of 20 for A and 24 for B. The shares at or below this time are 20/40 = 50% and 24/60 = 40% respectively. Group B has more students up to 20 minutes, while Group A has the greater share. Use the quantity the question asks for.
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Frequently asked questions
What if the vertical axis already shows cumulative percentages?
Use 75% for both curves. The graph has already converted each count to a share of its group.
Why write “about” in the answer?
A reading from a drawn curve is generally an estimate. Use a precision appropriate to the scale and how clearly you can read the intersection.