Frequency table

Introduction to frequency table math: Collection of observations is the first step in statistical investigations. The numerical observations collected by an observer cannot be put to any use immediately and directly. That is why it is called a raw data. The raw data when put in ascending or descending order of magnitude is called an array or arrayed data.

Frequency table definition

According to frequency table definition : A 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 table are of two types:
(i) Discrete frequency table distribution
(ii) Continuous or grouped frequency table distribution
Discrete frequency table distribution: The process of preparing this type of distribution is very simple. The construction of a discrete frequency distribution from the given raw data is done by the use of the method of tally marks. In the first column of the frequency table we write all possible values of the variable from the lowest to the highest.

Continuous or grouped table distribution: The above method of condensing the data is convenient only where the values in the raw data are largely repeating and the difference between the largest and the smallest observations is not very large.

How to do a frequency table?
If the number of observations is large, then arranging data in ascending or descending or serial order is a tedious job and it does not tell us much except perhaps the minimum and maximum of data.
Let us understand how to make a frequency table

In the first column of the table, we write all marks from lowest to highest. We now look at the first value in the given raw data and put a bar in the second column opposite to it. Now we see the second value in the given raw data and put a bar opposite to it in the second column. This process is repeated till all observations in the given raw data are exhausted. The bars drawn in the second column are known as tally marks and to facilitate we record tally marks in bunches of five, the fifth tally mark is drawn diagonally across the first four. We finally count the number of tally marks corresponding to each observation and write in the third column.
This way of representation of data is known as frequency distribution. Marks are called variates and the number of students who have secured a particular number of marks is called frequency of variate. The number of times an observation occurs in the given data, is called the frequency of observation.