Question

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. If the mean of the distribution is 7, find:
(a) the value of x;
(b) the standard deviation of their ages.

Accepted Answer

(a) Sum of frequencies (total children), Sigma-f = 2+6+5+x+6+9+8+5 = 41+x.
Sum of (age x frequency), Sigma-fx = 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.
Mean = Sigma-fx / Sigma-f = 7: (291+6x)/(41+x) = 7.
291+6x = 287+7x, so x = 4.

(b) With x=4, the frequency table is: Age(3,4,5,6,7,8,9,10), f(2,6,5,4,6,9,8,5), Sigma-f=45.
Deviations from the mean (7): -4,-3,-2,-1,0,1,2,3. Squared deviations: 16,9,4,1,0,1,4,9.
f x (deviation)^2: 32, 54, 20, 4, 0, 9, 32, 45. Sum = 196.
Standard deviation = sqrt(Sigma[f(x-mean)^2] / Sigma-f) = sqrt(196/45) = sqrt(4.3556) = 2.087 years (to 3 d.p.).

NECO Mathematics 2022 Theory — Question 10

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