Example

Example 1:

The average of five numbers is 29, if one number is exclude the average becomes 27. what is the exclude number ?
let the exclude number is
= ( 29 x 5 ) – ( 27 x 4 )
= 145 – 108
= 37.

The exclude number 37.

Example 2:

What would be the average of first 20 natural numbers ?
Sum of first n natural numbers = n ( n + 1 ) /2
So, we can find easily average of first 20 natural numbers 20 x 21 / 2 = 210
So, then Required average is = 210 / 20 = 10.5.

Example 3:

What would be the average of first 20 multiplies of 5.
Required average = 5 ( 1 + 2 + 3 +……………….. + 20) /20
= ( 5 x 20 x 21 / 20 x 2) = 2100 / 40 = 52.5.
So the Required average is 52.5.

Example 4 :

The average marks of 13 students is 40, the first six students is 30 and that of the last six students is 32. Find the value of the 7th number.
Shortcut tricks :
7th student marks number = Total of 13 students result – ( Total of first six students + Total of last six students results )
= 13 x 40 – ( 6 x 30 + 6 x 32 )
= 520 – 180 + 192
= 148.

Example 5

In a college, 16 girls has the average age is 18 years and 14 boys has the average age 17 years. What would be the average age of entire college ?
Answer: 16 girls has the average age is 18 years ( 16 x 18 ) = 288
4 boys has the average age 17 years ( 14 x 17 ) = 238
Average age is = 288 + 238 / 30 = 526 / 30 = 17.54 years