Frequency distribution with unequal class width is a significant statistical concept that requires understanding some basic terms. It is commonly used in economics for understandably presenting data. Let’s discuss in detail what frequency distribution with unequal class width is.

Variables. 

Categorized as continuous and discrete, variables are the ones whose values keep changing under the influence of several factors. These variables can be integers, decimals, rational, irrational, or whole. 

Continuous variables: Continuous variables can manifest every conceivable range of values in a given limit. These values can be broken down into infinite gradations. 

Discrete variables: Discrete variables can only take specific values. They cannot describe a range. 

Knowing variables and constants makes it easier to tabulate data and subsequently present it in different forms. Frequency distribution is a technique to classify raw data into a presentable format. You must have the data of any quantitative variable ready before starting to work on it. Let’s learn more about it. 

Frequency Distribution. 

It is a graphical or tabular way of representing organized data using a measurement scale. Using a frequency distribution, you can make out the intensity or concentration points of data, analyze the highs and lows, and derive firm conclusions for decision-making. If you need to observe the distribution of individual observations, using frequency distribution is the right way to go about it.

Common Terminologies

• Class Frequency: A class frequency meaning is a measure of the number of values present in one class. For example, if 5 students belong to the height range of 155 cm to 160 cm in a classroom, the class frequency for the 155-160 cm range is 5. 

• Class Limits: The upper and lower limits of a class are called the lower-class limit and the upper-class limit, respectively. 

• Class Width: The answer obtained after subtracting the lower-class limit from the upper-class limit is called the class width. 

• Class Mark or Class Midpoint: It is the sum of the upper and lower-class limits divided by 2. The middle value of a class represents the entire class. 

• Frequency Curve: The graphical representation of a frequency distribution on the X-axis and Y-axis is called a frequency curve. 

Frequency Distribution With Unequal Class Width 

For drawing a frequency curve, we use unequal class widths in two cases as listed below. 

• High Range of Data: In cases where the range of data is very high, it is not feasible to use classes of equal width. For example, the income of hundreds of people may vary from Rs. 100 per day to crores of rupees in a day. Such cases must be represented by the frequency distribution of unequal class widths. 

• Concentrated Values: If a particular class of data has a concentration of a high range of values, representing it using equal class widths will not give enough information for decision-making. It would suppress information at a particular class. 

Apart from these two cases, a distribution graph with equal class is generally used for data representation. 

Classes with unequal widths have class intervals that are of unequal magnitude. If you’re given a raw set of data and asked to choose between equal and unequal class widths, look at the frequency of the classes. If most of the observations are concentrated in some classes and the remaining classes are sparsely populated, a distribution graph with unequal width must be created. 

The observations in classes of equal width vary significantly from their class marks if they are incorrectly represented using a distribution graph of equal width. If you have to select a class mark for such a class, around which the data is largely concentrated, start creating a frequency distribution with unequal class width. 

Histogram

Frequency distribution is graphically represented using a histogram, which is a bar graph. The height of a histogram represents the class frequency, and its width represents the class interval. Unlike traditional bar graphs, the bars of a histogram are connected. This is because drawing traditional bar graphs aims to find similarities and differences between different variables. On the contrary, histograms display the distribution of variables on the X and Y axes. 

Histograms with Unequal Class Width 

If you are constructing a histogram with unequal class width, it is important to note that the areas of the rectangles drawn by the histogram must be proportional to the frequencies of every class. 

A histogram is a rectangle. One line of this rectangle is parallel to the baseline, and it is of the same length as the class interval. The vertical line of this rectangle is equal to the magnitude of the frequency density or frequency of the class. 

For classes with unequal widths, you must convert the classes into continuous ones for drawing a histogram. This is because a histogram cannot be drawn for discrete values or ranges. The upper limit of one class compulsorily touches the lower limit of the subsequent class in a histogram. People often skip drawing the common part between 2 rectangles to create a visible impression of continuity.  

Notably, through a histogram, you can graphically get the mode of a frequency distribution. 

Conclusion

Frequency distribution with an unequal class width can be easily done if you understand the following terms: 

• Class width 
• Class frequency 
• Class limits 
• Class mark 
• Frequency Curve 

Histograms help graphically represent frequency distribution using continuous class intervals in a bar graph format. The first step for graphically representing unequal class widths on a histogram is to convert the classes into continuous ones. With this data, it becomes easy to plot the histogram. From the graphical representation of a histogram, you can derive the mode of the data easily.