Grouped Frequency Distribution

Frequency distribution: Frequency table or frequency distribution is a method to

present raw data in the form from which one can easily understand the information contained in the raw data. Frequency distribution are of two types: (i) Discrete frequency distribution (ii) continuous or grouped frequency distribution.

Continuous or grouped frequency distribution. If the number of observations in data is large and the difference between the greatest and the smallest observations is large , then we condense the data into classes or groups. For example, let the marks obtained by 30 students of a class in a test be 39,25,5,33,19,21,12,48,13,21,9,1,10,8,12,17,19,17,41,40,12,46,37,17,27,30,6,2,23,19.we can arrange these marks as follows: Such a presentation of data is known as the grouped frequency distribution. In the above example 30 observations have been divided into 5 groups. These groups are called classes. The class 0-10 means the marks obtained between 0 and 10 including 0 and excluding 10. The number of observations falling in a particular class is called the frequency of that class or class frequency. Thus, the class 0-10 has frequency 6 and the class 10-20 has 11 as class frequency. In the class 0-10, we say that 0 is the lower limit and 10 is the upper limit of the class. Similarly in the class 10-20, 10 is the lower limit and 20 is the upper limit. The span of the class i.e., the difference between the upper limit and the lower limit, is known as the class interval. For example, in the class 10-20 the class interval is 20-10=10. There are two methods of classifying the data according to the class intervals, viz. (i) exclusive method, and (ii) inclusive" method.

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Constructing frequency distribution:

To construct frequency distribution from the given raw data we use the following algorithm. Algorithm . STEP 1 Obtain the given raw data. STEP 2 Prepare a table with three columns: first for variable under study such as marks, weight, height etc., second for Tally marks and third for the total, representing corresponding frequency to each value or size of the variable. STEP 3 Place all the values of the variable in the first column in ascending order. STEP 4 Take the first observation in the raw data and put a bar in the second column opposite to it. Then take the second observation in the given raw data and put a bar opposite to it. Continue this process till all the observations in the given raw data are exhausted. For the sake of convenience, record tally marks in bunches of five, the fifth is obtained by crossing diagonally the other four. Leave some space between each block of bars. STEP 5 Count the number of bars (tally marks) in respect of each value of the variable and place it in third column. STEP 6 Give a suitable title to the frequency distribution chart so that it conveys exactly what the chart is about.

by:Omkar Nayak

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