Ex.3.2 Q2 Data Handling - NCERT Maths Class 7

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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?

 Video Solution
Data Handling
Ex 3.2 | Question 2

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 \(= 15\) (6th observation)

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

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

  
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