# Ex.14.4 Q2 Statistics Solution - NCERT Maths Class 9

## Question

In a mathematics test given to \(15\) students, the following marks (out of \(100\)) are recorded:

\(41, 39, 48, 52, 46, 62, 54, \\ 40, 96, 52, 98, 40, 42, 52, 60.\)

Find the mean, median and mode of this data.

## Text Solution

**What is known?**

Marks obtained by \(15\) students in mathematics test

**What is unknown?**

Mean, median and mode.

**Reasoning:**

The mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations.

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.

The mode is that value of the observation which occurs most frequently.

**Steps:**

The marks obtained by \(15\) students in mathematics test:

\(41, 39, 48, 52, 46, 62, 54, \\40, 96, 52, 98, 40, 42, 52, 60.\)

Mean of data

\(\begin{align} &= \frac{ \text{sum of all observation}}{ \text{Total number of observation}} \\\\&= \frac{\begin{Bmatrix} 41 + 39 + 48 + 52 +\\ 46 + 62 + 54 + 40 +\\ 96 + 52 + 98 + 40 \\ + 42 + 52 + 60 \end{Bmatrix} }{15}\\&= \frac{822}{15}\\\\ &= 54.8\end{align}\)

Arranging them in ascending order we get:

\(39,40, 40, 41, 42, 46, 48, 52,\\ 52, 52, 54, 60, 62, 96, 98. \)

As the number of observations is \(15\) which is odd, therefore, the median of data will be \(\begin{align} \frac{{15 + 1}}{2}\end{align} = \) \(8\) ^{th }observation whether the data is arranged in an ascending or descending order.

Therefore, median score of data \(= 52\)

Mode of data is the observation with the maximum frequency in data. Therefore, mode of this data is \(52\) having the highest frequency in data as \(3\).