# Construction of Frequency Distribution

Following steps are involved in the construction of a frequency distribution.

(1) Find the range of the data: The range is the difference between the largest and the smallest values.

(2) Decide the approximate number of classes: Which the data are to be grouped. There are no hard and first rules for number of classes. Most of the cases we have $5$ to $20$ classes. H.A. Sturges has given a formula for determining the approximation number of classes.

Where $K$= Number of Classes
Where $\log N$ = Logarithm of the total number of observations.

For Example: If the total number of observations is $50$, the number of classes would be

$K = 1 + 3.322\log N$
$K = 1 + 3.322\log 50$
$K = 1 + 3.322(1.69897)$
$K = 1 + 5.644$
$K = 6.644$

$7$ Classes approximately.

(3) Determine the approximate class interval size: The size of class interval is obtained by dividing the range of data by number of classes and denoted by $h$ class interval size

In case of fractional results, the next higher whole number is taken as the size of the class interval.

(4) Decide the starting point: The lower class limits or class boundary should cover the smallest value in the raw data. It is a multiple of class interval.

For Example: $0$,$5$,$10$,$15$,$20$ etc… are commonly used.

(5) Determine the remaining class limits (boundary): When the lowest class boundary of the lowest class has been decided, then by adding the class interval size to the lower class boundary, compute the upper class boundary. The remaining lower and upper class limits may be determined by adding the class interval size repeatedly till the largest value of the data is observed in the class.

(6) Distribute the data into respective classes: All the observations are marked into respective classes by using Tally Bars (Tally Marks) methods which is suitable for tabulating the observations into respective classes. The number of tally bars is counted to get the frequency against each class. The frequency of all the classes is noted to get grouped data or frequency distribution of the data. The total of the frequency columns must be equal to the number of observations.