Question to find the maximum and minimum possible values of the average of a few numbers given some other parts of the jigsaw.
Mean and Range
Q.7: 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?
2.8 kgs
3.2 kgs
3 kgs
4 kgs
Correct Answer
Choice C. 3 kgs
Explanatory Answer
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Detailed Solution
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.
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.
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).
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.
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.
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)
Correct Answer: 3 kgs
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