Question

If the mean of 8, 12, 17, x and 23 is 16, find the value of x.​

Answer 1

Given :–

• Terms :- 8, 12, 17, x and 23.
• Mean of the terms :- 16.

To Find :–

• Value of x.

Solution :–

We know that,

$\boxed{mean = \dfrac{sum \: of \:all \: terms}{total \: terms} }$

Given,

• Mean = 16.
• Sum of all terms = 8 + 12 + 17 + x + 23.
• Total terms = 5.

Now, put all the terms in the formula of mean.

➠ $16 = \dfrac{8 + 12 + 17 + x + 23}{5}$

➠ $16 = \dfrac{20 + 17 + 23 + x}{5}$

➠ $16 = \dfrac{37 + 23 + x}{5}$

➠ $16 = \dfrac{60 + x}{5}$

➠ $16 \times 5 = 60+ x$

➠ $80 = 60+ x$

➠ $80 - 60 = x$

➠ $20 = x$

Hence,

The value of x is 20.

Check :–

Put all the values in the formula of mean.

Values,

• Terms :- 8, 12, 17, x and 23.
• Value of x = 20.
• Mean of the terms :- 16.
• Total terms :- 5.

➠ $\dfrac{8 + 12 + 17 + 20 + 23}{5} = 16$

➠ $\dfrac{20 + 37 + 23}{5} = 16$

➠ $\dfrac{43 + 37}{5} = 16$

➠ $\dfrac{ \cancel{80}}{ \cancel5} = 16$

➠ $16 = 16$

Since, the L.H.S. and the R.H.S. are equal.

So, the value of x is 20 is correct.