# Ex.3.2 Q2 Data Handling - NCERT Maths Class 7

## Question

The runs scored in a cricket match by \(11\) players are as follows: -

\(6, 15, 120, 50, 100,80, 10,15,\\ 8, 10, 15\)

Find the mean, median and mode of the data. Are they same?

## Text Solution

**What is known?**

Runs scored in a cricket match by \(11\) Players

**What is unknown?**

The mean, median and mode of the data

**Reasoning: \(\begin{align}\text{Mean}=\frac{\text{Sum of all scores}}{\text{Total no}\text{. of players}}\end{align}\)**

Mode** \(=\) **Mode is the observation that occurs highest number of times

Median\(=\)Median is the middle observation

**Steps: **

Total number of players \(= 11\)

Scores of players \(= 6, 15, 120, 50, 100,80, 10,15, 8, \\ \quad10, 15\)

\[\begin{align}{\rm{Mean}}& = \frac{{{\text{Sum of all scores}}}}{{{\text{Total no}}.{\text{of players}}}} \\ &= \frac{{\left[ \begin{array}{l}{\rm{6}} + {\rm{8}} + {\rm{1}}0 + {\rm{15}} + \\{\rm{15}} + {\rm{15}} + {\rm{5}}0 + {\rm{8}}0 + \\{\rm{1}}00 + {\rm{12}}0 \\\end{array} \right]}}{{11}} \\ &= \frac{{{\rm{429}}}}{{11}} \\ &= 39 \\\end{align}\]

Thus, mean \(= 39.\)

Arranging the scores into ascending order, we get

\(6, 8, 10,10, 15, 15,15, 50, 80, \\ 100, 120 \)

Mode is the observation that occurs highest number of times

Here, \(15\) occurs \(3\) times

\(∴\) Mode \(=15.\)

Median is the middle observation

\(∴\) Median \(= 15\) (6^{th} observation)

Thus, Mean \(=\) \(39\) , Mode \(=\) \(15\) and median \(=\) \(15\)

No, the mean, mode and median are not same.