ITPEC IP October 2018 Question 1
A survey into the amount of pocket money is conducted at three (3) schools. When the consolidated results of the survey are used to calculate the average pocket money per student for all the students of the three (3) schools, which of the following is the expression that is entered into cell C5?
Explanation
Total pocket money divided by the total number of students — the schools differ in size, so each school's total is rebuilt as its student count times its average.
The three averages cannot simply be averaged. Rebuild each school's total first:
- •School M: 150 × 1250 = 187500
- •School N: 250 × 850 = 212500
- •School P: 60 × 1530 = 91800
- •All schools: 491800 ÷ 460 students (150 + 250 + 60) ≈ 1,069 per student
In the sheet this is (B2*C2+B3*C3+B4*C4)/SUM(.
Answer (b)
Why not others:
- •(a) — multiplies the student counts together and divides by the product of the averages; neither product is an amount of money or a number of students, and the result is about 0.0014
- •(c) — adds the three averages (3,630) and divides by the number of students, about 7.9; a sum of averages is not a total amount of money
- •(d) — the simple mean of the three averages, 1,210, gives School P's 60 students the same weight as School N's 250
Key rule: To combine the averages of groups of different sizes, weight each by its size: the sum of (count × average) divided by the sum of the counts.
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