Question

13. The following are the marks scored by 20 students in a test:
15  11  17  25  13  15  16  22  24  27
20  22  15  16  15  19  22  24  22  11
(a) Prepare a frequency table for the distribution using class intervals 10−12, 13−15, 16−18...
(b) Calculate the variance of the distribution.
(c) If the pass mark for the test was 16, find the probability that a student selected at random from the class failed.

Accepted Answer

(a) Frequency table:
10−12: f=2, x=11, fx=22, fx²=242
13−15: f=5, x=14, fx=70, fx²=980
16−18: f=3, x=17, fx=51, fx²=867
19−21: f=2, x=20, fx=40, fx²=800
22−24: f=6, x=23, fx=138, fx²=3174
25−27: f=2, x=26, fx=52, fx²=1352
Σf=20, Σfx=373, Σfx²=7415

(b) Variance = Σfx²/Σf − (Σfx/Σf)²
   = 7415/20 − (373/20)² = 22.93

(c) P(fail, i.e. score < 16) = 7/20 = 0.35

WAEC Mathematics 2025 Theory — Question 19

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