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Feb/Mar 2017 p62 q4
2509
The weights in kilograms of packets of cereal were noted correct to 4 significant figures. The following stem-and-leaf diagram shows the data.
The weights in kilograms of packets of cereal were noted correct to 4 significant figures.
747
3
(1)
748
1 2 5 7 7 9
(6)
749
0 2 2 2 3 5 5 5 6 7 8 9
(12)
750
1 1 2 2 2 3 4 4 5 6 7 7 8 8 9
(15)
751
0 0 2 3 3 4 4 5 5 7 7 9
(13)
752
0 0 0 1 1 2 3 4 4 4
(11)
753
2
(1)
Key:748 | 5 represents 0.7485 kg.
On the grid, draw a box-and-whisker plot to represent the data.
Name a distribution that might be a suitable model for the weights of this type of cereal packet. Justify your answer.
Solution
Solution
(i) To draw the box-and-whisker plot, calculate the quartiles from the data:
Lower Quartile (LQ) = 0.7495
Median (Med) = 0.7507
Upper Quartile (UQ) = 0.7517
Draw a box from LQ to UQ with a line at the median.
Extend whiskers to the minimum and maximum values in the data set.
(See the mark scheme for the exact plot layout.)
(ii) A normal distribution is suitable because the data is approximately symmetrical, with most values clustered around the centre and tails tapering off quickly.