Draw a scatter plot on the grid provided in the ANSWER BOOK.
About this question
Question 2.1 of Mathematics Grade 12 Paper 2, NSC Examination (May/June) (DBE, May/June 2025). It tests the Term 3 ATP topic Statistics (Regression and Correlation).
- TermTerm 3
- ATP topicStatistics (Regression and Correlation)
- PaperPaper 2
- Marks3 marks
A supermarket recorded the number of items in 10 online orders and the time (in minutes) a packer took to get each order ready for delivery.
| Number of items (x) | 10 | 3 | 20 | 14 | 17 | 9 | 12 | 18 | 15 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|
| Time in minutes (y) | 5 | 5 | 9 | 7 | 6 | 6 | 8 | 11 | 10 | 12 |
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.
Other points that earn marks
- Marks are given for 3, 6 and all 10 points correct.
- Drawing a line through the points is not asked for.
More Questions On Statistics (Regression and Correlation)
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
Enter the data in the calculator in statistics (linear regression) mode.
\[a = 39{,}456\ldots \approx 39{,}46\]\[b = -0{,}590\ldots \approx -0{,}59\]\(\hat{y} = 39{,}46 - 0{,}59x\)
| Distance (\(x\) km) | Frequency | Cumulative frequency |
|---|---|---|
| \(0 \leq x \lt 5\) | 3 | 3 |
| \(5 \leq x \lt 10\) | 7 | 10 |
| \(10 \leq x \lt 15\) | 20 | 30 |
| \(15 \leq x \lt 20\) | 12 | 42 |
| \(20 \leq x \lt 25\) | 5 | 47 |
| \(25 \leq x \lt 30\) | 3 | 50 |
Cumulative frequencies: 3; 10; 30; 42; 47; 50
Median position:
\[\frac{1}{2} \times 60 = 30\text{th value}\]Reading across from 30 to the ogive and down: median \(\approx 65\) minutes
Enter the \(x\) and \(y\) values into the calculator (statistics, linear regression mode).
\[a = 39{,}47\]\[b = 1{,}44\]\(\hat{y} = 39{,}47 + 1{,}44x\)
Five-number summary: minimum 5 ; \(Q_1\) 44 ; median 65 ; \(Q_3\) 84 ; maximum 120.
Sketch: draw a box from 44 to 84 with a vertical line inside it at 65. Draw a whisker from the left side of the box to 5 and another from the right side of the box to 120.
Box: 44 to 84 with median at 65; whiskers to 5 and 120.