Complete the cumulative frequency column in the table provided in the ANSWER BOOK.
About this question
Question 2.1.2 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
- Marks2 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 \(91\%\).
Add each frequency to the running total:
| Class interval (%) | Frequency | Cumulative frequency |
|---|---|---|
| \(20 \lt x \leq 30\) | 8 | 8 |
| \(30 \lt x \leq 40\) | 14 | 22 |
| \(40 \lt x \leq 50\) | 16 | 38 |
| \(50 \lt x \leq 60\) | 21 | 59 |
| \(60 \lt x \leq 70\) | 16 | 75 |
| \(70 \lt x \leq 80\) | 9 | 84 |
| \(80 \lt x \leq 90\) | 6 | 90 |
| \(90 \lt x \leq 100\) | 2 | 92 |
Cumulative frequencies: 8; 22; 38; 59; 75; 84; 90; 92
More Questions On Statistics (Regression and Correlation)
The \(y\)-intercept says that an order with 0 items takes \(3{,}08\) minutes to pack.
It makes no sense to spend \(3{,}08\) minutes packing an order with no items.
\(Q_3\) position:
\[\frac{3}{4} \times 60 = 45\text{th value, so } Q_3 \approx 84 \text{ minutes}\]\[\text{IQR} = Q_3 - Q_1 = 84 - 44\]\(\text{IQR} = 40\) minutes
Ground the graph at \((0\,;\,0)\).
Plot the cumulative frequencies at the upper limits: \((5\,;\,3)\), \((10\,;\,10)\), \((15\,;\,30)\), \((20\,;\,42)\), \((25\,;\,47)\), \((30\,;\,50)\).
Join the points with a smooth, increasing S-shaped curve.
\(n = 92\), so the median is at a cumulative frequency of:
\[\frac{92}{2} = 46\]Read across from 46 to the curve and down to the \(x\)-axis.
\(\text{Median} \approx 54\%\)
\(27\%\)