Question

If the mean of 7, 9, X, 13, 6 is 8, find the value of X​

Answer 1

Answer:

$x=5$

Step-by-step explanation:

Given:-

Data = 7, 9, $x$, 13, 6

No. of data = 5

Mean = 8

To find:-

The value of $x$

Solution:-

Arithmetic Mean = Sum of all data ÷ No. of data

$8=\frac{7+9+x+13+6}{5}$

$8=\frac{35+x}{5}$

$8=\frac{35}{5} +\frac{x}{5}$

$8=7+\frac{x}{5}$

$8-7=\frac{x}{5}$

$\frac{x}{5} =1$

$x=1\times5$

$x=5$

∴ The value of $x$ is 5.

Answer 2

Answer:

X = 5

Step-by-step explanation:

We know that Mean is the sum of all observations divided by the total number of observations

The given observations are 7, 9, X, 13, 6

There are 5 observations (including X)

The sum of the given observations = 7 + 9 + X + 13 + 6

= 7 + 9 + 13 + 6 + X

= 35 + X

The mean of the given observations = ( Sum of all observations ) / ( Total number of observations )

= ( 35 + X ) / ( 5 )

But we are given that the Mean of the given observations is 8

=> ( 35 + X ) / ( 5 ) = 8

=> 35 + X = 8 * 5      ( Taking 5 in denominator of LHS to numerator of RHS )

=> 35 + X = 40

=> X = 40 - 35

=> X = 5

Therefore the value of X is 5

                                     

                                                      VERIFICATION:

The observations are 7, 9, X, 13, 6

But we have found out that X = 5

=> The observations are 7, 9, 5, 13, 6

There are 5 observations

=> Mean of the given observations = ( 7 + 9 + 5 + 13 + 6 ) / ( 5 )

= ( 40 ) / ( 5 )

= 8

Which matches the Mean given in the question

Hence verified that the value of X is 5