We provided some useful formulae and tips for Averages category.

An Average is defined as sum of the given observations divided by number of observations. It is also called as arithmetic mean. It is denoted by ‘A’.

=> Average = {Sum of given observation (S) / No. of observations (N)}

=> A = (S / N)

=> Average of first ‘n’ natural numbers = {n + 1} / 2

=> Average of first ‘n’ even numbers = (n + 1)

=> Average of first ‘n’ odd numbers = n

=> Average of consecutive numbers = {First number + Last number} / 2

=> Average of “1 to n” even numbers = {Last even number + 2} / 2

=> Average of “1 to n” odd numbers = {Last odd number + 1} / 2

Properties of Average:

1. If you observe result of average closely it should be less than the greatest observation and greater than smallest observation.

2. Suppose if the given observations are equal then the average is also be same as observation.

3. If the zero is one of the observations of given data we have to include that zero in the calculation.

4. If all the numbers get increased by ‘x’ then their average should be increased by ‘x’.This point is also applicable for subtraction, multiplication and divide properties.

Previous year solved Questions:

** 1. The average age of 3 men is 32 yr. If the age of fourth men is added, their average age comes out to be 31 yr. What is the age of the fourth men?**

A) 32 yr.

B) 28 yr.

C) 24 yr.

D) 26 yr.

E) None of these

Ans: B

Solution: Total age of 3 men = 32*3 = 96 yr.

Total age including the 4^{th} men = 31*4 = 124 yr.

Therefore age of fourth men = 124 – 96 = 28yr.

**2. Sachin has a certain average for 10 innings. In the eleventh innings, he scored 216 runs, thereby increasing his average by 12 runs. Find out new average?**

A) 96

B) 84

C) 97

D) 87

E) None of these

Ans: A

Solution: Assume average after 10^{th} innings = x

According to the given data, 10x + 216 = 11(x+12) => x=84

Therefore New average = 84 + 12 = 96