Question

A company manufactures car batteries of a particular type. The lives (in yrs) of 40 such 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 table for this data using class intervals of size 0.5 starting from the interval 2-2.5

Answer 1

Hint: ‘Size of class interval’ mentioned here refers to the gap or difference between the final and initial values of the respective class intervals where the data is grouped.
Class interval and size is already given, sort the data respectively and note it down in the table.

Complete step-by-step answer:
A frequency distribution is a representation, either in a graphical or tabular format, that displays the number of observations within a given interval. The interval size depends on the data being analyzed and the goals of the analyst. The intervals must be mutually exclusive and exhaustive. Frequency distributions are typically used within a statistical context. Generally, frequency distribution can be associated with the charting of a normal distribution.
According to the question, the class size is 0.5 , class intervals start from the interval 2-2.5. Using this information, we can count the values of respective classes and note the to make the table:

Lives of batteries	Tally	No. of batteries
2-2.5	||	2
2.5-3.0	|||| |	6
3.0-3.5	|||| |||| ||||	14
3.5-4.0	|||| |||| |	11
4.0-4.5	||||	4
4.5-5.0	||||	3

This is the grouped frequency distribution table of given data with class size as 0.5 starting from 2-2.5 and so on.

Note: The data can be arranged as increasing/ decreasing values before noting in the table (makes the work easier but is time consuming)
Be careful while counting variables lying between respective classes.