Draw a cumulative frequency curve (ogive) to represent the data above.
About this question
Question 2.1.3 of Mathematics Grade 12 Paper 2, NSC Examination (May/June) (DBE, May/June 2026). It tests the Term 3 ATP topic Statistics (Regression and Correlation).
- TermTerm 3
- ATP topicStatistics (Regression and Correlation)
- PaperPaper 2
- Marks3 marks
2.1 Marks (as a %) of Grade 12 learners at a school in the June 2025 Mathematics examination:
| Class interval (%) | Frequency |
|---|---|
| \(20 \lt x \leq 30\) | 8 |
| \(30 \lt x \leq 40\) | 14 |
| \(40 \lt x \leq 50\) | 16 |
| \(50 \lt x \leq 60\) | 21 |
| \(60 \lt x \leq 70\) | 16 |
| \(70 \lt x \leq 80\) | 9 |
| \(80 \lt x \leq 90\) | 6 |
| \(90 \lt x \leq 100\) | 2 |
2.2 A box and whisker diagram shows the marks (as a %) of learners at another school in the same examination. The five values labelled from left to right are: minimum \((x - 2)\%\), lower quartile \(\left(\frac{3x - 3}{2}\right)\%\), median \((2x + 5)\%\), upper quartile \((3x)\%\) and maximum \(91\%\).
Ground the curve at \((20\,;\,0)\), the lower boundary of the first class.
Plot each cumulative frequency at the upper boundary of its class: \((30\,;\,8)\), \((40\,;\,22)\), \((50\,;\,38)\), \((60\,;\,59)\), \((70\,;\,75)\), \((80\,;\,84)\), \((90\,;\,90)\), \((100\,;\,92)\).
Join the points with a smooth, increasing S-shaped curve.
Ogive from \((20\,;\,0)\) rising through the plotted points to \((100\,;\,92)\).
Other points that earn marks
- Plotting at the midpoints or lower limits of the classes loses the plotting mark.
- Not grounding the curve at \((20\,;\,0)\) loses a mark.
More Questions On Statistics (Regression and Correlation)
Plot number of items (\(x\)) on the horizontal axis and time (\(y\)) on the vertical axis.
Points to plot: \((10\,;\,5)\), \((3\,;\,5)\), \((20\,;\,9)\), \((14\,;\,7)\), \((17\,;\,6)\), \((9\,;\,6)\), \((12\,;\,8)\), \((18\,;\,11)\), \((15\,;\,10)\), \((19\,;\,12)\).
Ten correctly placed points; do not join them.
Enter the \(x\) and \(y\) values into the calculator (statistics, linear regression mode).
\[a = 39{,}47\]\[b = 1{,}44\]\(\hat{y} = 39{,}47 + 1{,}44x\)
\(27\%\)
About R216 455,60
This player scored far more runs than the other players who faced a similar number of balls (about 90 to 100 balls gave about 145 to 160 runs).