Frequency distribution:
The arrangement of data into groups or classes together with the number of observations in each group or class is called frequency distribution.
The number of observations falling (lying) in a particular class is called frequency and is usually denoted by (f). Data presented in the form of frequency distribution is also known as grouped data, while the data in original form is called ungrouped data while constructing a grouped frequency distribution. The following terms are associated with its construction. i.e. class limits, class boundaries, class mark, or midpoint of a class, width of a class or class interval size.
i. Class limits:
The pair of number of a variable which describe a class are called class limits. The smaller number is called the lower class limit while the larger number is called the upper class limit. The class limits are constructed in such a way that the upper limit of one class do not coincide with the lower limit of next higher class. Thus there is a gap between successive classes e.g. 10-19, 20-29, 30-39 etc.
ii. Class boundaries:
When class are constructed in such a way that the upper limit of one class coincides with the lower limit of next higher class, then such limits are called class boundaries. Thus there will be no gap between the successive classes. The class boundaries are exclusive.
e.g. 10-20, 20-30, 30-40, 40-50, etc hence 20 will be included in the class 20-30 instead of 10-20.
iii. Midpoint of a class or class mark:
The midpoint of a class is obtained by dividing the sum of upper and lower class limits/boundaries by 2. Since individual identity of the observation is lost in grouping process, hence for convenience of computation midpoint are compute, about midpoint of a class, we assume that each value in a class is equal to its midpoint e.g. if frequency of a class is 9 and its midpoint is 24, it means that all 9 values of a class are equal to 24.
iv. Width of a class or class interval size:
The different between successive lower limits or between successive upper limits is called width of class or class interval size. It may also be obtained by finding the difference between successive midpoints. The width of a class is usually denoted by (h).
Construction of frequency distribution:
While constructing a grouped frequency distribution the following steps should be taken into consideration.
i. For convenience arrange the data in an array using stem and leaf display.
ii. Determine the largest and smallest number from an arrayed data in order to find range i.e. the difference between largest and smallest number.
iii. Decide upon the number of classes. There is no hand and fast rule for deciding the number of classes, but a reasonable number of classes between 5 to 20 may be included depending upon the size of the data. Sturges also suggested a formula for deciding the number of classes i.e.
iii. Decide upon the number of classes. There is no hand and fast rule for deciding the number of classes, but a reasonable number of classes between 5 to 20 may be included depending upon the size of the data. Sturges also suggested a formula for deciding the number of classes i.e.
K = 1+3.3 log N
iv. To find the class interval size (h) divide the range by the desired number of classes e.g. if range of values is 87 and number of classes are 9, then class interval size will be 87/ 9 = 9.67 or approximately 10. Similarly if range is 43 and number of classes are 8, then class interval size will be 43/ 8 = 5.375 or 6 approximately (round off to next higher integer).
v. Decide what should be the starting value of the first class. The starting value is usually taken as the lowest value of the given data or less than that which is a multiple of 2 5, 10, and such other figures. The upper limit is obtained by adding the width of a class with the lower class limit. The remaining class limits are determined similarly.
vi. Distribute the values in to appropriate classes either by listing actual values In their proper classes or by using tally bars. The number of tallies is then written infrequency column.
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