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 0-5 (5 not included)
What main feature do you deserve from this tabular representation?

Answer 1

Hint: A certain range of data can be grouped together in certain classes which are known as class intervals. Class size is the difference between the final and initial values of the class interval.Here, take intervals 0-5 (given) and calculate the number of respective passengers falling in the respective intervals and make a tally column respectively to observe the trend.

Complete step-by-step answer:
Here, take intervals 0-5 (given) and calculate the number of respective passengers falling in the respective intervals and make a tally column respectively to observe the trend.

Distance (km)	Tally	No. of Engineers
0-5	||||	5
5-10	|||| |||| |	11
10-15	|||| |||| |	11
15-20	|||| ||||	9
20-25	|	1
25-30	|	1
30-35	||	2

 This is the frequency distribution table for the given data.
We observe:
I.Minimum number of engineers = 1; for both distance intervals 20-25 km and 25-30 km.
II.Maximum numbers of engineers = 11; for both distance intervals 5-10 km and 10-15 km.
III.Very few engineers have their home at more than an equal to 20 km.
IV.Most of the engineers have their homes at distance of 0-15 km

So, the correct answer is “Option C”.

Note: Class intervals are always uniform ( after 0-5 class interval 0-3 cannot take place because the size of the class should always remain 5)
Choose the class intervals wisely when not given.
Generally the last value of the respective intervals is excluded but take into consideration when specifically mentioned about inclusion or exclusion.