Histogram of Unequal Class Intervals
When histograms are drawn based on the data with unequal class intervals, they are known as Histograms of unequal class intervals. Histogram of unequal class intervals includes rectangles of different width sizes. Therefore, before drawing a histogram in case of unequal class intervals, frequency distribution has to be adjusted.
Adjustment of frequencies of unequal class intervals:
1. Determine the class of the smallest interval ( lowest class interval ).
2. Then, calculate the adjustment factor using the formula:
[Tex]Adjustment~Factor~for~any~Class=\frac{Class~Interval~of~the~Concerned~Class}{Lowest~Class~Interval} [/Tex]
3. Now, adjust the given frequencies using the adjustment factor:
[Tex]Frequency~Density=\frac{Given~Frequency}{Adjustment~Factor} [/Tex]
Example of Histogram of Unequal Class Intervals:
Present the following information in the form of a Histogram:
Wages | Number of Workers |
---|---|
10-15 | 14 |
15-20 | 20 |
20-25 | 54 |
25-30 | 30 |
30-40 | 24 |
40-60 | 24 |
60-80 | 16 |
Solution
1. It can be seen clearly that the given class interval is unequal. So, before plotting the histogram, frequencies have to be adjusted.
2. Determine the class of the smallest interval, i.e., 10-15. Thus, the lowest class interval in the given frequency distribution is 5.
3. Formulate the Adjusted Table as shown below:
Wages | Number of Workers | Adjustment Factor | Frequency Density |
---|---|---|---|
10-15 | 14 | 5 ÷ 5 = 1 | 14 ÷ 1 = 14 |
15-20 | 20 | 5 ÷ 5 = 1 | 20 ÷ 1 = 20 |
20-25 | 54 | 5 ÷ 5 = 1 | 54 ÷ 1 = 54 |
25-30 | 30 | 5 ÷ 5 = 1 | 30 ÷ 1 = 30 |
30-40 | 24 | 10 ÷ 5 = 2 | 24 ÷ 2 = 12 |
40-60 | 24 | 20 ÷ 5 = 4 | 24 ÷ 4 = 6 |
60-80 | 16 | 20 ÷ 5 = 4 | 16 ÷ 4 = 4 |
In the above table, the class interval is calculated as the difference between the upper-class limit and lower-class limit, i.e.,
15-10=5, 20-15=5, 20-25=5, 30-25=5, 40-30=10, 60-40=20, and 80-60=20.
4. Plotting Histogram:
Also Read:
Diagrammatic Presentation of Data: Meaning , Features, Guidelines, Advantages and Disadvantages
Bar Graph | Meaning, Types, and Examples
Pie Diagrams | Meaning, Example and Steps to Construct
Frequency Polygon | Meaning, Steps to Draw and Examples