Ex.3.2 Q1 Data Handling - NCERT Maths Class 7

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Question

The scores in mathematics test (out of \(25\)) of \(15\) students are follows: -

\(=\left[ \begin{align} & \text{19, 25, 23, 20, 9, 20, 15, 10,} \\ & \,\,\,\,\,\text{ 5,16, 25, 20, 24, 12, 20}\text{.} \\ \end{align} \right]\)

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

Text Solution

What is known?

Scores in mathematics test of \(15\) students

What is unknown?

The mode and median of the data

Reasoning:

Mode – Mode of a given data is that value of observation which occurs for the most 
number of times.
Median \(=\) middle of observation (in this case, \(8\)th observation)

Steps:

Scores of \(15\) students in mathematics test are \(=\left[ \begin{align}  & \text{19, 25, 23, 20, 9, 20, 15, 10,} \\  & \,\,\,\,\,\text{ 5,16, 25, 20, 24, 12, 20}\text{.} \\ \end{align} \right]\)

Arranging scores in ascending order, we get

\[\left[ \begin{align}  & \text{5, 9, 10, 12, 15, 16, 19, 20, } \\  & \,\,\text{20, 20, 20, 23, 24, 25, 25} \\ \end{align} \right]\]

Mode – Mode of a given data is that value of observation which occurs for the most

number of times.

Therefore\(, 20\) occurs most of the time.

\(∴\)  Mode \(= 20.\)

Median \(=\) middle of observation (in this case, \(8\)th observation)

\(∴\) Median \(= 20\)

Yes, mode and median of the given observations are same.

  
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