Ex.14.4 Q3 Statistics Solution - NCERT Maths Class 9

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Question

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

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

Text Solution

What is known?

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

What is unknown?

Value of \(x.\)

Reasoning:

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.

Steps:

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.

\[\begin{align}{\text{Therefore,}}\,{\text{median}}\,{\text{of the data}}\, &= \frac{{{5^{{\rm{th}}}}{\rm{observation}}\,{\rm{ + }}\,{6^{{\rm{th}}}}\,{\rm{observation}}}}{2}\\& \Rightarrow \,\,63 = \,\frac{{x + x + 2}}{2}\\&\Rightarrow \,\,63 = \,\frac{{2x + 2}}{2}\,\\&\Rightarrow \,\,63\, = \,x + 1\\& \Rightarrow \,\,x\, = \,62\end{align}\]

  
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