Ex.14.2 Q4 Statistics Solution - NCERT Maths Class 9

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Question

The heights of \(50\) students, measured to the nearest centimeters, have been found to be as follows:

\(161\,\,\,\, 150\,\,\,\, 154\,\,\,\, 165\,\,\,\, 168\,\,\,\, 161\,\,\,\, 154\,\,\,\, 162\,\,\,\, 150\,\,\,\, 151\\ 162\,\,\,\, 164\,\,\,\, 171\,\,\,\, 165\,\,\,\, 158\,\,\,\, 154\,\,\,\, 156\,\,\,\, 172\,\,\,\, 160\,\,\,\, 170\\ 153\,\,\,\, 159\,\,\,\, 161\,\,\,\, 170\,\,\,\, 162\,\,\,\, 165\,\,\,\, 166\,\,\,\, 168\,\,\,\, 165\\ 164\,\,\,\, 154\,\,\,\, 152\,\,\,\, 153\,\,\,\, 156\,\,\,\, 158\,\,\,\, 162\,\,\,\, 160\,\,\,\, 161\,\,\,\, 173\\ 166 \,\,\,\,161\,\,\,\, 159\,\,\,\, 162\,\,\,\, 167\,\,\,\, 168\,\,\,\, 159\,\,\,\, 158\,\,\,\, 153\,\,\,\, 154\,\,\,\, 159\)

  1. Represent the data given above by a grouped frequency distribution table,Taking the class intervals as \((160 – 165), (165 – 170),\) etc.
  2. What can you conclude about their heights from the table?

Text Solution

 

What is known?

  • The heights of \(50\) students in \(\rm cm.\)
  • Class size is \(5\) [from the given instruction of class intervals to be taken as \(160- 165, 165-170, 170-175\) …. and so on].

What is unknown?

  • Constructing a grouped frequency distribution table.
  • Making inferences and drawing conclusions from the data of “heights of students”.

Reasoning:

According to class interval we can check how many numbers lie in between , like this we can draw frequency distribution table and can be conclude about height from table.

Steps:

A grouped frequency distribution table with a class size of \(5,\) for the heights of \(50\) students can be constructed as follows:

Height (in cm) Number of Students (frequency)
\(150-155\) \(12\)
\(155-160\) \(9\)
\(160-165\) \(14\)
\(165-170\) \(10\)
\(170-175\) \(5\)
Total \(50\)

Since ‘\(150\)’ is the lowest value, we started the \(1\rm st\) class interval at \(150.\)

The following features / conclusions can be drawn from the table:

  • A majority of \(70\%\) of the students (\(35\) students) are below \(165\rm cm\) height.
  • Only a \(10\%\) of the students (\(5\) students) are at a height of \(170\rm cm\) or above.
  
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