General Mathematics Paper 2,Nov/Dec. 2010
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Question12

1. The table shows the distribution of masses of some bags of beans in a grains store.

 Mass (kg) 51 - 55 56 - 60 61 - 65 66 - 70 71 - 75 76 – 80 No of bags 7 10 24 6 2 1

Calculate, correct to one decimal place, the:

1. range;
2. mean deviation

of the distribution.

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Observation

This question was reported to be popular and well attempted by majority of the candidates. However, while they were able to obtain the mean, only a few of them could calculate the mean deviation. Some candidates were also reported to calculate the range by subtracting the class mid point in stead of subtracting the lower class boundary of the first class from the upper class boundary of the last interval which would have been 80.5 – 50.5 = 30 kg. To find the mean, candidates were expected to multiply each class mid point (x) by its corresponding frequency (f), add all the products together (Σfx) and divide the result by the total frequency (Σf) to obtain the mean ( ) i.e.  =  =  = 61.9 kg. The mean deviation was obtained by multiplying the absolute deviation of each class mid point from the mean by the corresponding class frequency (f|x - |), adding them together (Σf|x - |) and dividing by the total frequency which gave  =  = 4.1 correct to one decimal place.