The below mentioned article provides a note on frequency distribution.
For any statistical analysis, the handling with raw data requires some treatment, i.e., the classification of data to organise the available values in a more compact way. The frequency distribution presents the data very concisely indicating how frequently a variable occurs in a group of study.
Construction of Frequency Distribution Table:
If there are repetitions in individual values or items of any investigation, suitable frequency table can be formed. These frequency tables may be discrete or may be continuous in nature. The available raw data at first should be converted into arrayed data. For biostatistics the raw data are arranged in ascending order to make it arrayed data (Example-2).
Example 1:
Following raw data is obtained in an investigation. 100 pea plants bore pods ranging from 15 to 41 in a garden of pea plants (see Raw Data Table A):
Then for discrete frequency distribution table, the values of variables are written in one column and the repetition of that value is written against it which is the frequency (Table 9.1, 9.2).
But for continuous frequency distribution table, the values are grouped in fixed interval and then the frequency within that interval is observed and noted.
The number of classes or the range of class interval is an important factor for making this kind of frequency distribution table. There is no fixed rule for how many classes can be formed, generally it depends on observation of available data, minimum 3 classes and maximum 20 classes can be formed.
The size of class interval also depends on the range of data and the number of classes, it is equal to the difference between highest and lowest value divided by the number of classes,
i – H-L/K
where i = class interval K.
H = Highest value
L = Lowest value
K = number of classes.
Overlapping Frequency Distribution Table:
Values of variables are grouped in such a fashion that the upper limit of one class interval is represented in next class interval. In an example (Example 2), number of pods ranges from 15 to 41, the classes may be 15-17, 17-19, 19-21, etc. (Table 9.3).
Non-Overlapping Frequency Distribution Table:
Values of variables are grouped in such a fashion that the upper level of one class interval does not overlap the preceding class interval. In the above example, number of pods ranges from 15 to 41, the classes can be prepared like 15-17, 18-20, 21-23, etc. (Table 9.4).
Cumulative Frequency Distribution Table:
Cumulative frequency is determined by adding the frequency of a class interval with the frequency of the preceding class interval. The cumulative frequency table can be prepared from both the overlapping and non-overlapping frequency distribution table (Table 9.5, 9.6).
Relative Frequency:
This is calculated from the cumulative frequency against the total population or sample.
Relative frequency of a class = Cumulative frequency of that class/Total no. of sample.
Class Limit:
It is defined as two boundaries of a class, i.e., the highest and lowest values of a class, which can be represented by L1 and L2.
Mid-Value of Class-Interval:
The central point of a class interval is called its mid-value or mid-point of that class, which is obtained by using the following formula.
Mid – value of a class = L1 + L2/2