The document discusses calculating the maximum and minimum possible average weights for a class of 5 students given: - The average weight of the 4 lightest students is 40kg - The average weight of the 4 heaviest students is 45kg It determines that the maximum possible average is 44kg when one student weighs 60kg. The minimum possible average is 41kg when one student weighs 25kg. Therefore, the difference between the maximum and minimum possible average weights is 3kg.

1. Averages

2. Averages
In a class of 5 students, average weight of the 4 lightest students is
40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is
the difference between the the maximum and minimum possible
average weight overall?
(a) 2.8 kgs (b) 3.2 kgs
(c) 3 kgs (d) 4 kgs

3. Averages
Lets say that the students are named a, b, c, d and e, in increasing
order of weights. The average of a, b, c and d is 40 kg, whereas the
average of b, c, d and e is 45 kg.
The sum of a, b, c and d is 160 kg, and the sum of b, c, d and e is 180
kg.
In a class of 5 students, average weight of the 4 lightest students is
40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is
the difference between the the maximum and minimum possible
average weight overall?

4. Averages
What is the total weight of all the students?
There are two ways of looking at this.
a) 160 + e
b) 180 + a
Or, e is 20 more than a.
In a class of 5 students, average weight of the 4 lightest students is
40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is
the difference between the the maximum and minimum possible
average weight overall?

5. Averages
The total weight is 160 + e. So, the highest value of e will correspond
to the highest possible average. The highest possible value of e
occurs when it is 20 higher than the highest possible value for a,
which is 40 (all the first 4 scores are equal to 40).
In a class of 5 students, average weight of the 4 lightest students is
40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is
the difference between the the maximum and minimum possible
average weight overall?

6. Averages
So, the highest possible average is
160 + 60
5
= 44
This will be the case when the weights are 40 kgs, 40kgs, 40 kgs, 40
kgs and 60 kgs.
In a class of 5 students, average weight of the 4 lightest students is
40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is
the difference between the the maximum and minimum possible
average weight overall?

7. Averages
Conversely, the least possible value for the average occurs when a is
the least. This happens when e is the least too (since a is 20 less than
e).
The least possible value for e is 45 =
180
4
.
So, the least possible value for a would be 25.
In a class of 5 students, average weight of the 4 lightest students is
40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is
the difference between the the maximum and minimum possible
average weight overall?

8. Averages
The least possible average =
180 + 25
5
= 41
This will be the case when the weights are 25 kgs, 45kgs, 45 kgs, 45
kgs and 45 kgs. So, the difference between maximum possible and
minimum possible average = 3 kgs.
Answer choice (c)
In a class of 5 students, average weight of the 4 lightest students is
40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is
the difference between the the maximum and minimum possible
average weight overall?

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