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Unit 2: Classification of Data

upper limit is 20, then this class, written as 10-20, includes all the observations which are Notes
greater than or equal to 10 but less than 20. The observations with magnitude 20 will be
included in the next class.
2. Inclusive Method: Here all observations with magnitude greater than or equal to the
lower limit and less than or equal to the upper limit of a class are included in it.

The two types of class intervals, discussed above, are constructed for the data on the measurements
of diameter of a wire as shown below:

20 - 29 30 - 39 40 - 49 50 - 59 Total
8 15 10 7 40

Mid-Value of a Class

In exclusive types of class intervals, the mid-value of a class is defined as the arithmetic mean of
its lower and upper limits. However, in the case of inclusive types of class intervals, there is a
gap between the upper limit of a class and the lower limit of the following class which is
eliminated by determining the class boundaries. Here, the mid-value of a class is defined as the
arithmetic mean of its lower and upper boundaries. To find class boundaries, we note that the
given data on the measurements of diameter of a wire is expressed in terms of millimeters,
approximated upto two places after decimal. This implies that a value greater than or equal to
1.095 but less than 1.10 is approximated as 1.10 and, thus, included in the class interval 1.10 - 1.19.
Similarly, an observation less than 1.095 but greater than 1.09 is approximated as 1.09 and is
included in the interval 1.00-1.09. Keeping the precision of measurements in mind, various class
boundaries, for the inclusive class intervals, given above, can be obtained by subtracting 0.005
from the lower limit and adding 0.005 to the upper limit of each class. These boundaries are
given in the third column of the above table.

Construction of a Grouped Frequency Distribution for the Data on the Measurements
of Diameter of a Wire

Taking class intervals as 1.00 - 1.10, 1.10 - 1.20, etc. and counting their respective frequencies, by
the method of tally marks, we get the required frequency distribution as given below:

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