# Frequency Distribution

A frequency distribution is a tabular arrangement of data into classes according to size or magnitude along with corresponding class frequencies (the number of values which fall in each class).

Ungrouped Data or Raw Data

Data which have not been arranged in a systemic order is called ungrouped or raw data.

Grouped Data

Data presented in the form of a frequency distribution is called grouped data.

Array

The numerical raw data arranged in ascending or descending order is called an array.

Example:

Array the following data in ascending or descending order: 6, 4, 13, 7, 10, 16, 19.

Solution:

An array in ascending order is 4, 6, 7, 10, 13, 16, and 19
An array in descending order id 19, 16, 13, 10, 7, 6, and 4

Class Limits

The variant values of the classes or groups are called the class limits. The smallest value of the class is called the lower class limit and the largest value of the class is called the upper class limit. Class limits are also called inclusive classes.

Example: Let us take the class 10 – 19. The smallest value 10 is the lower class limit and the largest value 19 is the upper class limit.

Class Boundaries

The true values which describe the actual class limits of a class are called class boundaries. The smallest true value is called the lower class boundary and the largest true value is called the upper class boundary of the class. It is important to note that the upper class boundary of a class coincides with the lower class boundary of the next class. Class boundaries are also known as exclusive classes.

Example:

 Weight in Kg No of Students 60 – 65 8 65 – 70 12 70 – 75 5 25

A student whose weight is between 60kg and 64.5kg would be included in the 60 – 65 class. A student whose weight is 65kg would be included in the next class, 65 – 70.

Open-end Classes

A class which has no lower class limit or no upper class limit in a frequency table is called an open-end class. We do not like to use open-end classes in practice, because they create problems in calculation.

Example

 Weight in Pounds No of People Below – 110 6 110 – 120 12 120 – 130 20 130 – 140 10 140 – Above 2

Class Mark or Mid Point

The class mark or mid point is the mean of the lower and upper class limits or boundaries. It divides the class into two equal parts. It is obtained by dividing the sum of the lower and upper class limits or class boundaries of a class by 2.

Example: The class mark or mid point of the class 60 – 69 is 60+69/2 = 64.5

Size of Class Interval

The difference between the upper and lower class boundaries (not between the class limits) of a class or the difference between two successive mid points is called the size of class interval.