# How to Solve the Frequency Distribution Table?

The frequency distribution table helps us find patterns in the data and also enables us to analyze the data using central tendency and variance criteria.

## Step by step guide tothefrequency distribution table

Frequency distribution tables are a way to organize data in a way that makes the data more meaningful. A frequency distribution table is a graph that summarizes all data in two columns – variables/categories and their frequency. It has two or three columns. Usually, the first column lists all the results as separate values or as class intervals, depending on the size of the data set. The second column contains the counting scores of each result. The third column lists the frequency of each outcome. Also, the second column is optional.

### How to create a frequency distribution table?

Creating a frequency distribution table is easy using the following steps:

• Step 1: Create a table with two columns – one with the title of the data you organize and the other column for frequency. (Draw three columns if you want to add tally marks too)
• Step 2: Look at what is written in the data and decide whether you want to draw an ungrouped frequency distribution table or a group frequency distribution table. If there are many different values, it is usually best to go with a grouped frequency distribution table.
• Step 3: Write the data set values in the first column.
• Step 4: Count how many times each item is repeated in the collected data. In other words, find the frequency of each item by counting.
• Step 5: Write the frequency for each item in the second column.
• Step 6: At last you can also write the total frequency in the last row of the table.

Example: The following table shows the test scores of $$20$$ students:

The frequency distribution table drawn above is called the ungrouped frequency distribution table. This display is ungrouped data and is usually used for a smaller data set.

### What is a frequency distribution table in statistics?

Frequency distribution in statistics is the display of data that shows the number of observations within a given interval. The representation of a frequency distribution can be graphical or tabular.

Such graphs make it easier to understand the collected data.

• Bar graphs show data using bars of uniform width with equal distances between them.
• A pie chart shows a whole circle, divided into sectors where each sector is proportional to the information it represents.
• A frequency polygon is plotted by joining the midpoints of the bars in a histogram.

### Frequency distribution table for grouped data

The frequency distribution table for grouped data is known as grouped frequency distribution table. This is based on the frequency of class intervals. In this table, all data categories are divided into different class intervals of the same width, for example, $$0-10, 10-20, 20-30,$$ and so on. And then the frequency of that class interval is marked against each interval.

See an example of a frequency distribution table for grouped data in the image below.

### Cumulative frequency distribution table

Cumulative frequency means the sum of the frequencies of the class and all classes below it. We can calculate by adding the frequency of each class lower than the corresponding class interval or category. The following is an example of a cumulative frequency distribution table:

### Frequency Distribution Table– Example 1:

A school held a blood donation camp. Blood groups of $$30$$ students were registered as follows. Display this data in the form of a frequency distribution table.

$$A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, A, O, B, A, B, O, O, A, A, O, O, AB, B$$

Solution:

We can display the above data in the frequency distribution table as follows:

## Exercises forFrequency Distribution Table

Below the weekly pocket expenses (in dollars) a group of $$25$$ students was selected at random:

$$37,\:41,\:39,\:34,\:41,\:26,\:46,\:31,\:48,\:32,\:44,\:39,\:35,\:39,\:37,\:49,\:27,\:37,\:33,\:38,\:49,\:45,\:44,\:37,\:36$$

Create a grouped frequency distribution table with class intervals of equal widths, starting from $$25 – 30, 30 – 35$$, and so on.

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