Ex.14.2 Q2 Statistics Solution - NCERT Maths Class 9

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Question

The distance (in km) of \(40\) engineers from their residence to their place of work were found as follows:

\(5\,\,\,\, 3\,\,\,\, 10\,\,\,\, 20\,\,\,\, 25\,\,\,\, 11\,\,\,\, 13\,\,\,\, 7\,\,\,\, 12\,\,\,\, 31\\ 19\,\,\,\, 10\,\,\,\, 12\,\,\,\, 17\,\,\,\, 18\,\,\,\, 11\,\,\,\, 32\,\,\,\, 17\,\,\,\, 16\,\,\,\, 2\\ 7\,\,\,\, 9\,\,\,\, 7\,\,\,\, 8\,\,\,\, 3\,\,\,\, 5\,\,\,\, 12\,\,\,\, 15\,\,\,\, 18\,\,\,\, 3\\ 12\,\,\,\, 14\,\,\,\, 2\,\,\,\, 9\,\,\,\, 6\,\,\,\, 15\,\,\,\, 15\,\,\,\, 7\,\,\,\, 6\,\,\,\, 12\)

Construct a grouped frequency distribution table with class size \(5\) for the data given above taking the first interval as \(0-5\) (\(5\) not included). What main features do you observe from this tabular representation?

Text Solution

 

What is known?

  • The distance in \(\rm km\) of \(40\) engineers from their residence to work.
  • Class size of \(5\) [ class size refers to the count of data that has to be accommodated in each grouping of data]
  • Class interval as \(0-5\) (\(5\) not included).

What is unknown?

Main features of the tabular representation to be drawn from the given data.

Reasoning:

By drawing frequency distribution we can observe main features

Steps:

Since the given data is large, we need to group the data into classes of size each \(5\) and construct a table which will make the important features of the data visible.

This table is known as grouped frequency distribution table.

The class intervals will be \(0-5, 5-10, 10-15\) and so on.

The distance (in \(\rm km\)) of \(40\) engineers from their residence to their place work can be represented as follows (with the help of tally marks.)

DISTANCE (in \(\rm km\)) TALLY MARKS NO OF ENGINEERS (frequency)
\(0-5 \) |||| \(5 \)
\(5-10 \) |||| |||| | \(11\)
\(10-15\) |||| |||| | \(11\)
\(15-20 \) |||| | | | | \(9 \)
\(20-25 \) | \(1 \)
\(25-30 \) | \(1\)
\(30-35\) || \(2\)
Total   \(40\)

The following features can be observed from the table.

  • \(5\) engineers have their houses below \(5\,\rm km\) distance from work place.
  • A majority of engineers (\(36\)) have their houses below \(20\,\rm km\) distance from work place.
  • Only a few engineers (\(4\)) have their houses at \(20\,\rm km\) and above distance from work place.
  
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