Question

10(a) The table shows the distribution of ages of a number of children in a school.
Age (years): 3,4,5,6,7,8,9,10
Number of children: 2,6,5,x,6,9,8,5
Of the mean of the distribution is 7, find the: (a) value of x; (b) standard deviation of their ages.

Accepted Answer

(a) Mean = Σfx/Σf.
Σf = 2+6+5+x+6+9+8+5 = 41+x
Σfx = 3(2)+4(6)+5(5)+6(x)+7(6)+8(9)+9(8)+10(5) = 6+24+25+6x+42+72+72+50 = 291+6x
7 = (291+6x)/(41+x)
7(41+x) = 291+6x
287+7x = 291+6x
x = 4.

(b) Using the frequency distribution with x=4:
Age(x): 3,4,5,6,7,8,9,10; Frequency(f): 2,6,5,4,6,9,8,5; x−x̄: −4,−3,−2,−1,0,1,2,3; (x−x̄)²: 16,9,4,1,0,1,4,9; f(x−x̄)²: 32,54,20,4,0,9,32,45
Σf(x−x̄)² = 196
Σf=45
Standard deviation δ = √(Σf(x−x̄)²/Σf) = √(196/45) = √4.356 = 2.087.

WAEC Mathematics 2022 Theory — Question 10

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