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June 2008 p6 q1
2378
The stem-and-leaf diagram below represents data collected for the number of hits on an internet site on each day in March 2007. There is one missing value, denoted by \(x\).
Stem-and-leaf diagram:
Stem
leaf
0
0156
(4)
1
135668
(6)
2
112344489
(9)
3
1222x89
(7)
4
25679
(5)
Key: \( 1 \mid 5 \) represents 15 hits.
(i) Find the median and lower quartile for the number of hits each day.
(ii) The interquartile range is 19. Find the value of \(x\).
Solution
(i) To find the median, we need to arrange the data in order and find the middle value. There are 31 data points (including \(x\)). The median is the 16th value, which is 24.
The lower quartile (LQ) is the median of the first half of the data. The first 15 values are considered, and the 8th value is 16.
(ii) The interquartile range (IQR) is given as 19. The upper quartile (UQ) is calculated as \(\text{LQ} + 19 = 35\). The value of \(x\) must be 5 to maintain the order and achieve the correct UQ.