Quants 4 - Average

Key Points to Remember:

Average = Sum of observations / Number of observations
Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then the average speed during the whole journey is 2xy / (x + y) kmph

Practice Questions:

Question 1:

Find the average of all prime numbers between 30 and 50.

There are 5 prime numbers between 30 and 50.
They are 31, 37, 41, 43 and 47.
Average = ( 31 + 37 + 41 + 43 + 47 ) / 5 = 199 / 5 = 39.8
Thus, average of all prime numbers between 30 and 50 is 39.8.

Question 2:

Find the average of the first 40 natural numbers.

Sum of n natural numbers = [ n(n+1) ] / 2
Sum of first 40 natural numbers = ( 40 * 41 ) / 2 = 820
Average = 820 / 40 = 20.5
The average of the first 40 natural numbers is 20.5.


Question 3:

Find the average of first 20 multiples of 3.
Required average = [ 3 * ( 1 + 2 + 3 + ... + 18 + 19 + 20 ) ] / 20 = ( 3 * 20 * 21 ) / ( 20 * 2 )
= 1260 / 40 = 31.5
The average of first 20 multiples of 3 is 31.5.


Question 4:
The average of four consecutive even numbers is 27. Find the largest of these numbers.
Let the numbers be x, x+2, x+4, x+6.
[ x + (x+2) + (x+4) + (x+6) ] / 4 = 27
x + (x+2) + (x+4) + (x+6) = 108
4x + 12 = 108
4x = 96
x = 96 / 4 = 24
Hence, the largest number is x + 6 = 24 + 6 = 30.
The largest of the 4 consecutive numbers whose average is 27 is 30.


Question 5:

There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of section A is 40 kg and that of section B is 35 kg. Find the average weight of the whole class.

Total weight of 36 + 44 students = ( 36 * 40 ) + ( 44 * 35 ) = 1440 + 1540 = 2980 kg
Average of whole class = 2980 / (36 + 44) = 2980 / 80 = 37.25 kg
The average weight of the whole class is 37.25 kg.


Time to Think:

David obtained 76, 65, 82, 67 and 85 marks out of 100 in English, Math, Physics, Chemistry and Biology. What is his average mark?