Explain the construction of frequency distribution with the help of an example.

1. Introduction

Frequency distribution is a statistical technique used to organize and summarize data by grouping it into categories and recording the number of occurrences (frequency) within each category. It provides a clear visual representation of the distribution of data, making it easier to analyze and interpret patterns and trends. This method is particularly useful when dealing with large datasets or continuous data.

2. Example Dataset

Let's consider an example dataset of exam scores obtained by students in a class:

80, 75, 85, 90, 65, 75, 80, 70, 95, 85, 75, 80, 85, 90, 70, 75, 80, 85, 90, 85

3. Determining the Range

Before constructing the frequency distribution, it's essential to determine the range of the dataset. The range is the difference between the maximum and minimum values.

Maximum value = 95

Minimum value = 65

Range = Maximum value – Minimum value

Range = 95 – 65 = 30

The range of the dataset is 30.

4. Determining the Number of Intervals

The number of intervals or classes for the frequency distribution should be chosen carefully to effectively represent the data without losing important information. Commonly used guidelines include Sturges' Rule or the Square Root Rule.

Sturges' Rule:
Number of classes = 1 + log2(n)

Where 'n' is the number of data points.

For our example dataset:
Number of classes ≈ 1 + log2(20) ≈ 1 + 4.32 ≈ 5.32

Since we can't have a fraction of a class, we round up to the nearest integer.
Number of classes ≈ 6

5. Determining the Class Width

The class width is the range of values covered by each interval. It is calculated by dividing the range by the number of classes.

Class Width = Range / Number of classes

Class Width = 30 / 6 = 5

The class width of each interval is 5.

6. Constructing the Frequency Distribution Table

Using the determined number of classes and class width, we can now construct the frequency distribution table.

7. Counting Frequencies

Next, we count the frequencies by tallying the occurrences of data points within each interval.

For the given dataset, the frequencies are:

8. Representing the Frequency Distribution Graphically

Finally, the frequency distribution can be represented graphically using histograms or frequency polygons, providing a visual summary of the distribution of data.

Conclusion

In conclusion, constructing a frequency distribution involves determining the range, selecting the number of intervals, calculating the class width, creating a frequency distribution table, counting frequencies, and representing the distribution graphically. This method is valuable for summarizing large datasets and identifying patterns and trends within the data.