Past papers › WAEC · 2021 · May/June · General Maths · Paper 2 › Question 11 Question WAEC General Maths 2021 Theory Statistics: data & averages Dispersion & cumulative frequency Statistics: data & averages, Dispersion & cumulative frequency
WAEC 2021 · Paper 2 · Q11
Number of hours per day
4
5
6
7
8
9
10
11
Number of students
5
7
5
9
12
4
3
5
The table shows the distribution of the number of hours per day spent in studying by 50 students. Calculate, correct to two decimal places, the:
(a) (b) Worked solution (try it first) Use an assumed mean of 8 hours, with
d = x − 8 d = x - 8 d = x − 8 :
x x x 4
5
6
7
8
9
10
11
Total
f f f 5
7
5
9
12
4
3
5
50
d d d − 4 -4 − 4 − 3 -3 − 3 − 2 -2 − 2 − 1 -1 − 1 0
1
2
3
f d fd f d − 20 -20 − 20 − 21 -21 − 21 − 10 -10 − 10 − 9 -9 − 9 0
4
6
15
− 35 -35 − 35
f d 2 fd^2 f d 2 80
63
20
9
0
4
12
45
233
(a) Mean
= 8 + − 35 50 = 8 − 0.7 = 7.30 = 8 + \frac{-35}{50} = 8 - 0.7 = 7.30 = 8 + 50 − 35 = 8 − 0.7 = 7.30 hours.
(b) Standard deviation
= ∑ f d 2 ∑ f − ( ∑ f d ∑ f ) 2 = \sqrt{\frac{\sum fd^2}{\sum f} - \left(\frac{\sum fd}{\sum f}\right)^2} = ∑ f ∑ f d 2 − ( ∑ f ∑ f d ) 2 = 233 50 − ( − 0.7 ) 2 = \sqrt{\frac{233}{50} - (-0.7)^2} = 50 233 − ( − 0.7 ) 2 = 4.66 − 0.49 = \sqrt{4.66 - 0.49} = 4.66 − 0.49 ≈ 2.04 \approx 2.04 ≈ 2.04 hours.
Watch out
Check each row of the table before adding: a single wrong entry spoils the standard deviation. f d 2 fd^2 f d 2 f × d 2 f \times d^2 f × d 2 d d d f f f Report a problem with this question