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 General Mathematics Paper 2, May/June. 2011
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 Main
Weakness/Remedies
Strength

Question 11

The table shows the scores obtained when a fair die was thrown a number of times.

 Score 1 2 3 4 5 6 Frequency 2 5 x 11 9 10

If the probability of obtaining a 3 is 0.26, find the

1. median;
2. standard deviation of the distribution.
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Observation

The Chief Examiner reported that although this question was popular among the candidates, majority of them could not obtain the value of x which showed poor knowledge of the concept of probability. Others were not able to handle the fractions involved. Candidates were expected to obtain the total frequency as 2 + 5 + x + 11 + 9 + 10 = 37 + x. Since the probability of a 3 is 0.26, then  = 0.26. By cross multiplying and bringing like terms together, we obtain x = 13.
333
Thus, the total frequency becomes 50. The median = average of the 25th and 26th score = 4.    From the table,

 Score (x) Frequency f fx fx2 1 2 2 2 2 5 10 20 3 13 39 117 4 11 44 176 5 9 45 225 6 10 60 360 Total Σf = 50 Σfx = 200 Σfx2 = 900

Standard deviation =  = 1.41