The mean of the 5 smallest numbers from a group is 15 while the mean of all the numbers of the group taken together is 17. If the mean of the numbers leaving the smallest five out is 18.25, how many numbers were there in the group in all?

Question

Question

This question was previously asked in

RRB ALP CBT I 29 Aug 2018 Shift 2 Official Paper

Answer 1

Given:

The mean of the 5 smallest numbers from a group is 15

The mean of all the numbers of the group taken together is 17

The mean of the numbers leaving the smallest five out is 18.25

Concept used:

Average = Sum of elements/Number of elements

Calculation:

Let there be x numbers.

Sum of smallest 5 numbers = 5 × 15

⇒ 75

Sum of all the numbers = 17x

Sum of numbers leaving the smallest five out = (x – 5) × 18.25

⇒ 18.25x - 91.25

Sum of numbers leaving the smallest five out + Summation of smallest 5 numbers = Summation of all the numbers

⇒ 18.25x – 91.25 + 75 = 17x

⇒ 1.25x = 16.25

⇒ x = 16.25/1.25

⇒ x = 13

So, there are total 13 numbers

∴ The required answer is 13.

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