In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!

Ex.14.4 Q3 Statistics Solution - NCERT Maths Class 9

Go back to  'Ex.14.4'


The following observations have been arranged in ascending order. If the median of the data is \(63,\) find the value of \(x.\)

\(29, 32, 48, 50, x, x + 2, 72, 78, 84, 95\)

 Video Solution
Ex exercise-14-4 | Question 3

Text Solution

What is known?

Ungrouped data and median of data is \(63.\)

What is unknown?

Value of \(x.\)


The median is that value of the given number of observations, which divides it into exactly two parts. So, when the data is arranged in ascending (or descending) order the median of ungrouped data can be calculated based on no. of observation are even or odd.


It can be observed that the total number of observations in the given data is \(10\) (even number).

Therefore, the median of this data will be the mean of \(\begin{align} \frac{{10}}{2}\end{align} \) i.e., \(5\)th and \(\begin{align} \frac{{10}}{2}\end{align} \)  \(+ 1\) i.e., \(6\)th observation.

Therefore, median of the data

\(\begin{align}   &= \frac{ \begin{Bmatrix} 5^{\rm th}  \text{observation } + \\  6^{\rm th}  \text{ observation} \end{Bmatrix} }{2}\\& \Rightarrow \,\,63 = \,\frac{{x + x + 2}}{2}\\&\Rightarrow \,\,63 = \,\frac{{2x + 2}}{2}\,\\&\Rightarrow \,\,63\, = \,x + 1\\& \Rightarrow \,\,x\, = \,62\end{align}\)

Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school