Estimate the interquartile range.
About this question
Question 2.3 of Mathematics Grade 12 Paper 2, NSC Examination (DBE, November 2024). It tests the Term 3 ATP topic Statistics (Regression and Correlation).
- TermTerm 3
- ATP topicStatistics (Regression and Correlation)
- PaperPaper 2
- Marks2 marks for the method (formula and substitution) and the correct final answer
The ogive (cumulative frequency graph) shows the time taken (in minutes) by 60 employees to travel to work each morning.
Diagram: time in minutes (0 to 140) on the horizontal axis and cumulative frequency (0 to 65) on the vertical axis. The curve starts at \((0\,;\,0)\), passes through about \((20\,;\,5)\), \((40\,;\,13)\), \((60\,;\,26)\), \((80\,;\,41)\), \((100\,;\,56)\) and levels off at \((120\,;\,60)\).
\(Q_3\) 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
More Questions On Statistics (Regression and Correlation)
New frequencies: 3; 11; 20; 8; 5; 3
\[\text{Estimated mean} = \frac{2{,}5(3) + 7{,}5(11) + 12{,}5(20) + 17{,}5(8) + 22{,}5(5) + 27{,}5(3)}{50}\]\[= \frac{675}{50}\]\(= 13{,}5\text{ km}\)
Use the calculator in linear regression mode (\(A + Bx\)).
\[a = 3{,}079\ldots\]\[b = 0{,}351\ldots\]\(\hat{y} = 3{,}08 + 0{,}35x\)
\(Q_1\) is at the \(12{,}5\)th position and \(Q_3\) at the \(37{,}5\)th position. Read these off the ogive:
\[Q_1 \approx 11\text{ km}\]\[Q_3 \approx 17{,}8\text{ km}\]\[\text{IQR} = Q_3 - Q_1 = 17{,}8 - 11\]\(\text{IQR} \approx 6{,}8\text{ km}\)
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.
\(Q_1\) position:
\[\frac{1}{4} \times 60 = 15\text{th value}\]\(Q_1 \approx 44\) minutes
\(27\%\)