If 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41 are ten observation in an ascending order with median 24

Question:

If 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41 are ten observation in an ascending order with median 24, find the value of x.

Solution:

10, 13, 15, 18, x+1, x+3, 30, 32, 35 and 41 are arranged in ascending order.
Median = 24
We have to find the value of x.
Here, n is 10, which is an even number.
Thus, we have:

Median $=$ Mean of $\left(\frac{n}{2}\right)$ th \& $\left(\frac{n}{2}+1\right)$ th observations

$\therefore$ Median $=$ Mean of $\left(\frac{10}{2}\right)$ th $\&\left(\frac{10}{2}+1\right)$ th observations

$=$ Mean of 5 th \& 6 th observations

$=\frac{1}{2}(x+1+x+3)$

$=\frac{1}{2}(2 x+4)$

$=(x+2)$

Given :

Median $=24$

$\Rightarrow x+2=24$

$\Rightarrow x=22$

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