Question

The mean of 8 numbers is 32. If one more number is included, the new mean becomes 31. Find the included number

Answer 1

Answer:

27

Step-by-step explanation:

Since the mean of four numbers is 32.

Therefore, the sum of all four numbers is (4×32)=128

Now,one more number is added then,

The mean becomes 31.

So,new sum of 5 numbers (5×31)=155

Therefore,the new number=155-128

=27

Answer 2

Given:

The mean of 8 numbers is 32. If one more number is included, the new mean becomes 31.

To find:

The included number.

Solution:

The included number is 23.

To answer this question, we will follow the following steps:

As we know that an average or mean of 'n' observations is equal to the sum of 'n' observations divided by the total number of observations.

This means,

$mean \: = \frac{sum \: of \: 'n' \: observations}{n}$

As given, we have

The mean of 8 numbers = 32

This means

$\frac{sum \: of \: 8 \: numbers}{8} = 32$

So,

Sum of 8 numbers = 256

Now,

One number is included, let it be x.

So,

Sum of 9 numbers = 256 + x

Total numbers = 9

New mean = 31

So,

$\frac{sum \: of \: 9 \: numbers}{9} = 31$

$\frac{256 + x}{9} = 31$

$256 + x = 279$

$x = 23$

Hence, the included number is 23.