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.
If the mean of the data $3, 21, 25, 17, (x + 3), 19, (x - 4)$ is 18, then find:
i) the value of $x$ ,
ii) the median of the data.

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Solution

i)
$M e a n = \frac{s u m o f o b s e r v a t i o n}{t o t a l n o . o f o b s e r v a t i o n}$
$18 = \frac{3 + 21 + 25 + 17 + x + 3 + 19 + x - 4}{7}$
$126 = 84 + 2 x$
$2 x = 42$
$x = 21.$

ii)
Now to find the median of given data, first arrange the given data in ascending order.
Ascending order of the given data $= 3, 17, 17, 19, 21, 24, 25.$
Median of odd number of data = $\frac{1}{2} \times (n + 1) t h$ observation.
Therefore,
Median = $\frac{1}{2} \times (7 + 1) t h = 4 t h o b s e r v a t i o n .$
Median = $19.$ [ $4 t h o b s e r v a t i o n = 19$ ]

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