Further Mathematics Paper 2, May/June. 2012
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength

Question 14

The table gives the distribution of heights in metres of 100 students

 Height 1.40 -1.42 1.43-1.45 1.46-1.48 1.49-1.51 1.52-1.54 1.55-1.57 1.58-1.60 1.61-1.63 Frequency 2 4 19 30 24 14 6 1

(a)      Calculate the:
(i)   mean height;
(ii)   mean deviation of the distribution.

(b)     What is the probability that the height of a student selected at random is greater than the mean height of the distribution?

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Observation

This question was reported to have been attempted by majority of the candidates and their performance was commended by the Chief Examiner.  Solving this problem was simplified by obtaining the following table:

 Height f Mid-point x fx |d| = |x - mean| f|d| 1.40 – 1.42 2 1.41 2.82 0.1023 0.2046 1.43-1.45 4 1.44 5.76 0.0723 0.2892 1.46-1.48 19 1.47 22.93 0.0423 0.8037 1.49-1.51 30 1.50 45 0.0123 0.369 1.52-1.54 24 1.53 36.72 0.0177 0.4248 1.55-1.57 14 1.56 21.84 0.0477 0.6678 1.58-1.60 6 1.59 9.54 0.0777 0.4662 1.61-1.63 1 1.62 1.62 0.1077 0.1077 Total 100 151.23 3.333