Estimate the median travel time.
About this question
Question 2.1 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
- Marks1 mark 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 \((120\,;\,60)\).
Median position:
\[\frac{1}{2} \times 60 = 30\text{th value}\]Reading across from 30 to the ogive and down: median \(\approx 65\) minutes
More Questions On Statistics (Regression and Correlation)
Use the calculator in linear regression mode (\(A + Bx\)).
\[a = 3{,}079\ldots\]\[b = 0{,}351\ldots\]\(\hat{y} = 3{,}08 + 0{,}35x\)
Use the calculator in linear regression (STAT, \(A + Bx\)) mode with the 10 data pairs.
\[a = -43{,}72\]\[b = 2{,}36\]\(\hat{y} = -43{,}72 + 2{,}36x\)
Enter the data in the calculator in STAT mode (A + BX), with \(x\) = age and \(y\) = price.
\[a = 331\,397{,}20\]\[b = -22\,988{,}32\]\(\hat{y} = 331\,397{,}20 - 22\,988{,}32x\)
\(n = 92\), 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.
\(\text{Median} \approx 54\%\)
About 255 runs (\(255{,}28\) if the unrounded calculator values are used)