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Nov 2013 p61 q4
2493
The following are the house prices in thousands of dollars, arranged in ascending order, for 51 houses from a certain area.
253
270
310
354
386
428
433
468
472
477
485
520
520
524
526
531
535
536
538
541
543
546
548
549
551
554
572
583
590
605
614
638
649
652
666
670
682
684
690
710
725
726
731
734
745
760
800
854
863
957
986
Draw a box-and-whisker plot to represent the data.
For the above data, give the prices of the expensive houses.
Give one disadvantage of using a box-and-whisker plot rather than a stem-and-leaf diagram to represent this set of data.
An expensive house is defined as a house which has a price that is more than 1.5 times the interquartile range above the upper quartile.
Solution
(i) Draw a box-and-whisker plot on a linear scale (thousands of dollars). Mark the lower quartile, median, upper quartile, and whisker endpoints correctly.
(ii) Compute the interquartile range (IQR) and the outlier fence:
Lower quartile: \(Q_1 = 538\), Upper quartile: \(Q_3 = 690\).
\(\text{IQR} = Q_3 - Q_1 = 690 - 538 = 152\).
\(\text{Upper fence} = Q_3 + 1.5\,\text{IQR} = 690 + 1.5\times 152 = 918.\)
Any price \(> 918\) is “expensive”. Hence the expensive houses are \(957\) and \(986\) (thousands of dollars).
(iii) A box-and-whisker plot does not display individual data values, so detailed distribution features (like gaps or clustering) are hidden.