Question

If the mean of the data 3,21, 25, 17, (x+ 3), 19, (x- 4) is 18, find the value of x. Using this value of x, find the median of the data.​

Answer 1

$Mean=\frac{Sumofobservations}{Totalno.ofobservations}$.
$18=\frac{3+21+25+17+x+3+19+x-4}{7}$.

$18\times 7=2x+84$
$\Rightarrow 126=2x+84$
$\Rightarrow 2x=126-84$
$\Rightarrow 2x=42$
$\Rightarrow x=21$

Thus, the value of ‘x’ is 21.

Now, putting the value of ‘x’ equal to 21 in the given observations.

So, the observations are 3, 21, 25, 17, 24, 19, 17.

Arrange the following observations in ascending order.

So, numbers are 3, 17, 17, 19, 21, 24, 25.

Total number of observations is 7.

Since, n is odd we have to use the formula to calculate the median of the given observations.
median of odd number of data = $\frac{n+1}{2}$observations.
Median = $\frac{7+1}{2}$observation.
Median = $4$ observation.
Median = 19 ( 4th observation = 19)

Thus, the median of the given observations is 19.