A company manufactures car batteries of a particular type. The life (in years) of 40 batteries were recorded as follows:

2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5

3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7

2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8

3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4

4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6

Construct a grouped frequency distribution table with exclusive classes for this data, using class intervals of size 0.5 starting from the interval 2 - 2.5.

Given are life (in years) of 40 batteries.

Know that, when the lower limit is included, but the upper limit is excluded, then it is an exclusive class interval. For example – 150-153, 153-156, etc … are exclusive type of class intervals. In the class interval 150 - 153, 150 is included but 153 is excluded.
Usually in the case of continuous variate, exclusive type of class intervals are used.

We can arrange the data in ascending order since the data is very large. We have

2.2, 2.3, 2.5, 2.6, 2.6, 2.8, 2.9, 2.9, 3.0, 3.0, 3.1, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 3.3, 3.4, 3.4, 3.4, 3.5, 3.5, 3.5, 3.5, 3.6, 3.7, 3.7, 3.7, 3.8, 3.8, 3.9, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.6

This makes calculation of frequencies easier.

So, let the class interval start from 2.0.

Then, add 0.5 to 2.0 = 2.0 + 0.5 = 2.5

⇒ First class interval = 2.0-2.5

Similarly,

Second class interval = 2.5-3.0 [∵, 2.5 + 0.5 = 3.0]

And so on…

For frequencies, count the occurrence of the numbers lying between the particular class interval.

Let us construct a table in order to show these class intervals along with their frequencies.

Thus, this is the required frequency distribution table.