# RELATIVE FREQUENCY OF A CLASS INTERVAL

## About "Relative frequency of a class interval"

Relative frequency of a class interval may be defined as the ratio of the class frequency to the total frequency.

To have better understanding on relative frequency of a class interval, let us consider the frequency distribution given below.

In the above frequency distribution of weights of 36 students, the relative frequencies for the first two class intervals are 3/36 and 4/36 respectively.

Apart from "Relative frequency of a class interval", let us look at some other important terms associated with a frequency distribution.

## Percentage frequency

Percentage frequency of a class interval may be defined as the ratio of class frequency to the total frequency, expressed as a percentage.

In the above frequency distribution of weights of 36 students, the percentage frequencies for the first two class intervals are 300/36 and 400/36 respectively.

It is quite obvious that whereas the relative frequencies add up to unity, the percentage frequencies add up to one hundred.

## Frequency density of a class interval

It may be defined as the ratio of the frequency of that class interval to the corresponding class length.

In the above frequency distribution of weights of 36 students, the frequency densities for the first two class intervals are

3/5 and 4/5

That is, 0.60 and 0.80 respectively.

## Class limit and class boundary in statistics

To understand class limit and class boundary in statistics, let us consider the frequency distribution of weights of 36 students given below.

## Class limit

Corresponding to a class interval, the class limits may be defined as the minimum value and the maximum value the class interval may contain.

The minimum value is known as the lower class limit (LCL) and the maximum value is known as the upper class limit (UCL).

For the frequency distribution of weights of 36 students, the LCL and UCL of the first class interval are 44 kgs. and 48 kgs. respectively.

## Class boundary

Class boundaries may be defined as the actual class limit of a class interval.

For overlapping classification or mutually exclusive classification that excludes the upper class limits like 10–
20, 20–30, 30–40, ……… etc. the class boundaries coincide with the class limits.

This is usually done for a continuous variable. However, for non-overlapping or mutually inclusive classification that includes both the class limits like 0–9, 10–19, 20–29,…… which is usually applicable for a discrete variable, we have

where D is the difference between the LCL of the next class interval and the UCL of the given class interval.

For the data presented in the above table, LCB of the first class interval

and the corresponding UCB

Apart from the stuff class limit and class boundary, let us look at the mid point of a class interval.

## Mid point or Mid value or Class mark

Corresponding to a class interval, this may be defined as the total of the two class limits or class boundaries to be divided by 2.

In other words, in a class interval, mid point or mid value may be defined as arithmetic mean or average of the two class limits and two class boundaries.

Thus, we have

Referring to the distribution of weight of 36 students, the mid-points for the first two class intervals are

That is, 46 kgs. and 51 kgs. respectively.

After having gone through the stuff given above, we hope that the students would have understood "Relative frequency of a class interval".

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