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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
General Comments
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.
_____________________________________________________________________________________________________
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

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