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3. Construction of frequency distribution table using grouped data

Class interval and Class size:

Class interval or classes is the difference between the upper limit and the lower limit. The upper limit is the class's highest value, and the lower limit is the class's lowest value.

The difference between the successive upper limits or the successive lower limits is called as the class size or the class width.

Example:

Let us construct a frequency distribution table for the following

$26$ data using tally marks.

$31, 32, 52, 60, 37, 49, 42, 56, 43, 55, 72, 84, 67, 75, 44, 41, 59, 57, 91, 98, 78, 66, 81, 88, 86, 58$

Sol:

We can see that the data is very large, and the reader find it difficult to understand it. Hence, let us group the given data.

The minimum value is

$31$ , and the maximum value is

$91$ . We shall group the data as

$30 - 39$ ,

$40 - 49$ , ...,

$90 - 99$ , which are called as class intervals.

Consider the classes

$30 - 39$ and

$40 - 49$ to find the class size.

Consider the successive upper limits, then the class size

$= 40 - 30 = 10$

Now, we shall tabulate the data.

Class interval	Tally marks	Frequency
$30 - 39$		$3$
$40 - 49$		$5$
$50 - 59$		$6$
$60 - 69$		$3$
$70 - 79$		$3$
$80 - 89$		$4$
$90 - 99$		$2$

This table is called a frequency distribution table using grouped data.

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3. Construction of frequency distribution table using grouped data

Theory: