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