Examples on Averages 1

In this class, we discuss Examples on Averages 1.

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Average = sum of all the values/number of values.

Example:

Average of 1,2,3 = (1+2+3)/ 3

Average 0f 1,2,3 = 6/3 = 2

Important: sum of all the values = Average * number of values

Most of all, the examples are based on the above equation.

If we know the average value and the number of values, we can find the sum of all the values.

Example 1:

The average of four consecutive even numbers is 27. find the largest of the numbers?

Solution:

Assume the numbers are x, x+2, x+4, x+6

Average = summation of all the numbers/number of numbers

(x+ x+2+ x+4+x+6)/4 = 27

(4x + 12)/4 = 27

x + 3 = 27

x = 30

The largest number = x + 6 = 30+6 = 36

Example 2:

There are two sections, A and B, of a class consisting of 36 and 40 students, respectively.

Section A and B’s average weight is 40 and 35 kg, respectively.

Find the average weight of the class.

Solution:

From the above formula, if the average value and number of values are provided, we can find the sum of values.

the sum of all the weights of section A is 36 * 40

the sum of all the weights of section B is 44 * 35

sum of all the weights of class is (36 * 40) + (44 * 35) = 2980

Average weight of the class = 2980/(36 + 44)

The average weight of the class = 37.25

Example 3:

Nine people went to the hotel to take their meals.

Eight of them spent Rs 12 each on their meals, and the 9th spent Rs 8 more than the average expenditure of all 9.

What is the total money spent?

Solution:

The average value is not given.

First, find the average value then we get the sum of all the values from the above formula.

Assume average = x

(12 * 8 + x+8)/9 = x

8x = 104

x = 13

Total spent = 9 * x = 9*13 = 117.