Question

The median of $\dfrac{x}{5}$, $\dfrac{x}{4}$, $\dfrac{x}{3}$, $\dfrac{x}{2}$, $x$$\left( {x > 0} \right)$ is $8$, then find the value of x.
a) $24$
b) $32$
c) $8$
d) $16$
e) $40$

Answer 1

Hint: Median is the middle number in a sorted, ascending or descending, list of numbers and in case of a data system, the median is also based on the frequency of the data. We are given the median of five numbers consisting of variable x and we have to find the value of x. So, we will first find the value of median in x and then equate it with the given value.


Complete step by step solution: 
Given numbers are: $\dfrac{x}{5}$, $\dfrac{x}{4}$, $\dfrac{x}{3}$, $\dfrac{x}{2}$, $x$. $\left( {x > 0} \right)$
So, x is a positive number.
Hence, we can arrange all the five given numbers in ascending order as follows:
$\dfrac{x}{5}$, $\dfrac{x}{4}$, $\dfrac{x}{3}$, $\dfrac{x}{2}$, $x$
Now, the middle value from the five values arranged in ascending order is the median of the data.
So, the median of the five observations is $M = \dfrac{x}{3}$.
Also, we are given that the median is equal to $8$.
Hence, $M = \dfrac{x}{3} = 8$
$ \Rightarrow \dfrac{x}{3} = 8$
$ \Rightarrow x = 24$
Therefore, the value of $x$is $x = 24$.

Note: Median is a measure of central tendency, just as mean and mode. Mean is the average of all observations and is calculated by dividing the sum of all observations by the number of all observations. Mode is the maximum recurring value. Median of a continuous data set can be calculated using the formula $M = I + \dfrac{{\dfrac{N}{2} - cf}}{f} \times h$
Where, I is the lower limit of the median class, N is the total frequency, cf is the cumulative frequency of previous class to the median class, f is the frequency of median class, h is the width of the median class.