Question

The mean of 6 numbers is 52. If one more number is included the mean of a new number is 54. Find the included number

Answer 1

The number added is 66

This Explanation may help you

Answer 2

Given,

The mean of 6 numbers = 52

The changed mean when a new number is added = 54

To find,

The newly included number.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the newly included number is x.

Mathematically,

The mean of a set of given data can be calculated as follows;

The mean = (sum of all the observations)/(total number of observations)

{Statement-1}

Now, according to the question;

The mean of 6 numbers = 52

=> (sum of all the observations)/(total number of observations) = 52

=> (sum of all the initial 6 observations)/6 = 52

=> sum of all the initial 6 observations = 312

{Equation-1}

Now, when a new number is included;

The mean of 7 numbers = 52

=> (sum of all the initial 7 observations)/7 = 54

=> sum of all the initial 7 observations = 378

{Equation-2}

So, the newly added 7th number

= (sum of all the initial 7 observations) - (sum of all the initial 6 observations)

= 378 - 312

= 66

Hence, the newly included number is 66.