# 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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