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Nov 2009 p61 q4
2498
A library has many identical shelves. All the shelves are full and the numbers of books on each shelf in a certain section are summarised by the following stem-and-leaf diagram.
3
6 9 9
(4)
4
6 7
(2)
5
0 1 2 2
(4)
6
0 1 1 2 3 4 4 4 5 5 6 6 6 7 8 9
(20)
7
1 1 3 3 3 5 6 7 8 9 9
(12)
8
0 2 4 5 5 6 8
(7)
9
0 1 2 4 4 4 5 5 6 7 7 8 8 9 9
(18)
Key: \( 3 \mid 6 \) represents 36 books.
Find the number of shelves in this section of the library.
Draw a box-and-whisker plot to represent the data.
In another section all the shelves are full and the numbers of books on each shelf are summarised by the following stem-and-leaf diagram.
2
1 2 2 3 3 4 5 6 6 6 7 9
(13)
3
0 1 1 2 3 4 5 6 6 7 7 8 8
(15)
4
2 2 3 5 7 8 9
(8)
Key: \( 3 \mid 6 \) represents 36 books.
There are fewer books in this section than in the previous section. State one other difference between the books in this section and the books in the previous section.
Solution
(i) Count the total number of leaves in the first stem-and-leaf diagram:
\(4 + 2 + 4 + 20 + 12 + 7 + 18 = 67\)
Thus, there are 67 shelves in this section of the library.
(ii) To draw a box-and-whisker plot, we need the quartiles:
Lower Quartile (LQ) = 64
Median = 73
Upper Quartile (UQ) = 90
Draw the box-and-whisker plot using these quartiles and the minimum and maximum values from the data.
(iii) The books in the second section have a smaller interquartile range (IQR) or standard deviation, indicating less variability in the number of books per shelf compared to the first section.