Frequency Distributions

What is a Frequency Distribution?

A frequency distribution is a table that shows how often different values occur in a dataset. It helps to organize data to see patterns and trends easily.

For example, if you survey students about their favorite fruit, a frequency distribution can show how many students prefer each type of fruit.

Components of a Frequency Distribution Table

• Class Intervals: These are the ranges of values in which data is grouped.
• Frequency: The number of times a data point appears within a class interval.
• Midpoint: The average of the upper and lower boundaries of a class interval.
• Cumulative Frequency: The running total of frequencies up to the end of each class interval.

Steps to Construct a Frequency Distribution Table

1. Decide on the number of classes: Typically between 5 and 20, depending on the data size.
2. Determine the class interval: Subtract the smallest data value from the largest and divide by the number of classes.
3. Create class intervals: Start from the smallest data value and add the class interval to find the next boundary.
4. Tally the data: Count how many data points fall into each class interval.
5. Record frequencies: Write down the frequency for each class interval.

Example

Constructing a Frequency Distribution Table

Consider the following data set of test scores: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90.