Write down the correlation coefficient of the data.
About this question
Question 2.3 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
- Marks1 mark
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 |
\(r = 0{,}74\)
More Questions On Statistics (Regression and Correlation)
Plot two points from the equation, for example:
\(x = 90\):
\[\hat{y} = -43{,}72 + 2{,}36(90) = 168{,}68\]\(x = 150\):
\[\hat{y} = -43{,}72 + 2{,}36(150) = 310{,}28\]Join the points with a straight line that covers the data range, from about \(x = 85\) to \(x = 160\).
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.
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.
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.
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.