Question

the median of the observation 11 12 14 18 x+2 x+4 30 32 35 41 arrange in ascending order is 24 find the value of x

Answer 1

we know,
if the number of observation (n) is even
then,
1. first of all find the value at the position $\{\frac{n}{2}\}$
2. and find the value at the position $\{\frac{n}{2}+1\}$
3. now find the average of two value to get the median .
e.g., $\text{median}=\frac{\{\frac{n}{2}\}th+\{\frac{n}{2}+1\}th}{2}$

Given, 11, 12, 14, 18, (x + 2), (x + 4) , 30, 32 , 35 , 41 are in ascending order .
number of terms = 10 {even}

so, median = {(n/2)th + (n/2 + 1) th }/2
24 = (5th + 6th)/2
24 = {(x + 2) + (x + 4)}/2
24 = (x + 3)
x = 21

hence, x = 21

Answer 2

The observation are already arranged in order  

so the middle two observations are x + 2 and x + 4

thus (x+2+x+4)/2=24

2x+6=48

2x=42

x=21.

Explanation: The median is a simple measure of central tendency.

To find the median, we arrange the observations in order from smallest to largest value.

If there are an odd number of observations, the median is the middle value.

If there is an even number of observations, the median is the average of the two middle values.