Write down the modal class interval for the data.
About this question
Question 2.1.1 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
- Marks1 mark
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 \(91\%\).
The highest frequency is 21.
\(50 \lt x \leq 60\)
More Questions On Statistics (Regression and Correlation)
\(\bar{x} = R\,570{,}27\)
Use the calculator in linear regression mode (\(A + Bx\)).
\[a = 3{,}079\ldots\]\[b = 0{,}351\ldots\]\(\hat{y} = 3{,}08 + 0{,}35x\)
Find the frequency of each class by subtracting consecutive cumulative frequencies:
\(0 \lt t \leq 20\): \(16\); \(20 \lt t \leq 40\): \(40 - 16 = 24\); \(40 \lt t \leq 60\): \(59 - 40 = 19\); \(60 \lt t \leq 80\): \(67 - 59 = 8\); \(80 \lt t \leq 100\): \(70 - 67 = 3\)
Draw bars with no gaps: \(x\)-axis Time, \(t\) (minutes) marked 0, 20, 40, 60, 80, 100; \(y\)-axis Number of people.
Bar heights 16, 24, 19, 8, 3 for the five classes, bars touching.
The gradient \(b = -22\,988{,}32\) gives the change in price per year.
R22 988,32 per year
Enter the data in the calculator in statistics (linear regression) mode.
\[a = 39{,}456\ldots \approx 39{,}46\]\[b = -0{,}590\ldots \approx -0{,}59\]\(\hat{y} = 39{,}46 - 0{,}59x\)
Premiums in this interval: \(325;\ 326;\ 362;\ 429;\ 515;\ 531;\ 598;\ 610;\ 624;\ 728\)
10 premiums