How to Solve the Frequency Distribution Table?

How to solve the frequency distribution table, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

A frequency distribution table organizes raw data into a compact format that shows how often each value (or range of values) occurs. It is one of the most practical tools in statistics and appears on the GED Math test in problems about reading tables, finding averages from summarized data, and interpreting patterns. Once you understand how to build and read one, you can extract mean, mode, and totals quickly.

What Is a Frequency Distribution Table?

A frequency distribution table has two main columns:

• Values (or Classes) — the individual data values or intervals of values
• Frequency — the count of how many times each value/class appears in the data

A third column for relative frequency ((color{blue}{text{ frequency } div text{ total }})) is sometimes added to show percentages.

Types of Frequency Distribution Tables

Ungrouped Frequency Table

Used when data values are individual numbers. Each unique value gets its own row.

Grouped Frequency Table

Used when there are many different values. Data is grouped into class intervals (e.g., 10–19, 20–29). Each row shows the interval and how many values fall in it.

How to Create a Frequency Distribution Table

Step-by-Step Process

1. List all the data values (for ungrouped) or choose class intervals (for grouped).
2. Tally how many times each value or class appears in the raw data.
3. Write the tally count as the frequency in the table.
4. Add a total row at the bottom: the sum of all (color{blue}{text{ frequencies } = text{ total }}) number of data points.

Finding the Mean from a Frequency Table

Multiply each value (x) by its frequency (f), add all products, then divide by total frequency:

Mean = Σ((color{blue}{x times f})) ÷ Σf

Step-by-Step Summary

1. Identify values or class intervals.
2. Count occurrences (tally) and record as frequencies.
3. Sum frequencies to get the total count.
4. To find the mean: compute Σ((color{blue}{x times f})) ÷ Σf.
5. To find the mode: find the value/class with the highest frequency.

Watch: How to Construct a Frequency Distribution Table (Video Lesson)

The Organic Chemistry Tutor explains how to build a frequency distribution table step by step:

Worked Examples

Example 1: Create a frequency table for: 3, 5, 3, 7, 5, 5, 3, 7, 9, 5.

(color{blue}{text{ Mean } = 52 div 10}) = 5.2; Mode = 5 (frequency 4, the highest)

Example 2: A frequency table shows: Score 80 ((color{blue}{f = 2})), Score 85 ((color{blue}{f = 3})), Score 90 ((color{blue}{f = 4})), Score 95 ((color{blue}{f = 1})). What is the total number of students? What is the mean score?

(color{blue}{text{ Total } = 2 + 3 + 4 + 1}) = 10 students
Σ(color{blue}{(x times f) = 80(2) + 85(3) + 90(4) + 95(1) = 160 + 255 + 360 + 95 = 870})
(color{blue}{text{ Mean } = 870 div 10}) = 87

Example 3: What is the mode from a table where: 10 appears 3 times, 20 appears 5 times, 30 appears 2 times?

Mode = 20 (highest frequency of 5)

Example 4: From a grouped table: ages 20–29 ((color{blue}{f=5})), 30–39 ((color{blue}{f=8})), 40–49 ((color{blue}{f=4})), 50–59 ((color{blue}{f=3})). Which age group is most common?

The 30–39 age group has the highest frequency (8). 30–39 is the modal class.

More Practice: Grouped Frequency Distribution Tables (Video)

Math with Mr. J demonstrates how to create a grouped frequency distribution table:

Exercises

1. Data: 2, 4, 2, 6, 4, 4, 8, 2, 6, 4. Create a frequency table.
2. Using your table from #1, find the mean and mode.
3. A frequency table shows: 1 ((color{blue}{f=5})), 2 ((color{blue}{f=3})), 3 ((color{blue}{f=2})). Find the total and the mean.
4. Which value is the mode in a table with: A(4), B(7), C(7), D(2)?
5. Scores: 70((color{blue}{f=3})), 80((color{blue}{f=5})), 90((color{blue}{f=2})). Find the mean score.
6. Add a relative frequency column to: Value 10((color{blue}{f=2})), Value 20((color{blue}{f=3})), Value 30((color{blue}{f=5})). ((color{blue}{text{ Total } = 10}))

Answers

1. Value 2((color{blue}{f=3})), Value 4((color{blue}{f=4})), Value 6((color{blue}{f=2})), Value 8((color{blue}{f=1})); (color{blue}{text{ Total } = 10})
2. Σ(color{blue}{(text{ xf }) = 2(3)+4(4)+6(2)+8(1) = 6+16+12+8 = 42}); (color{blue}{text{ Mean } = 42div 10}) = 4.2; Mode = 4
3. (color{blue}{text{ Total } = 5+3+2}) = 10; Σ(color{blue}{(text{ xf }) = 1(5)+2(3)+3(2) = 5+6+6 = 17}); (color{blue}{text{ Mean } = 17div 10}) = 1.7
4. B and C are both modes (both have frequency 7; this is bimodal)
5. Σ(color{blue}{(text{ xf }) = 70(3)+80(5)+90(2) = 210+400+180 = 790}); (color{blue}{text{ Mean } = 790div 10}) = 79
6. 10: (color{blue}{frac{2}{10} = 0.20}) (20%); 20: (color{blue}{frac{3}{10} = 0.30}) (30%); 30: (color{blue}{frac{5}{10} = 0.50}) (50%)

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Frequently Asked Questions

What is a frequency distribution table?

A frequency distribution table organizes raw data by listing each value, or each range of values, next to how many times it appears. For the quiz scores 7, 8, 8, 9, 9, 9, 10, the table shows 7 with a frequency of 1, 8 with 2, 9 with 3 and 10 with 1. The frequencies add up to 7, the number of scores, which is a quick way to check your table.

How do you solve a frequency distribution step by step?

List the values or choose class intervals, tally how often each one appears, and write the tallies as frequencies. Add a total row and check that it matches the number of data values. Then add any columns the question needs: relative frequency (f ÷ total), cumulative frequency (a running total) or fx (value × frequency) for finding the mean.

How do you find fx in a frequency distribution table?

Multiply each value x by its frequency f. If the value 4 appears 6 times, its fx is 4 × 6 = 24. For grouped data, use the midpoint of each class as x, so the class 10–19 with a frequency of 5 has a midpoint of 14.5 and fx = 14.5 × 5 = 72.5. The total of the fx column, Σfx, is what you divide by the total frequency to find the mean.

How do you find the mean in a frequency distribution table?

Divide Σfx by Σf. Suppose 2 students read 1 book, 5 read 2 books and 3 read 4 books. The fx values are 2, 10 and 12, so Σfx = 24 and Σf = 10. The mean is 24 ÷ 10 = 2.4 books. A common mistake is dividing by the number of rows (3) instead of the total frequency (10).

How do you calculate cumulative frequency in a frequency distribution table?

Keep a running total of the frequencies from the top row down. If the frequencies are 3, 5, 4 and 2, the cumulative frequencies are 3, 8, 12 and 14. The last cumulative frequency always equals the total number of data values, 14 here. Each cumulative frequency tells you how many values fall at or below that row, which helps when finding the median.

How do you find the median in a frequency distribution table?

Use the cumulative frequency to find the middle position. With 14 data values, the median is the average of the 7th and 8th values. For the values 1, 2, 3, 4 with frequencies 3, 5, 4, 2, the cumulative frequencies are 3, 8, 12, 14, so the 7th and 8th values both fall in the row for 2. The median is 2.

Related Topics

• Line Plot
• Distributions in Line Plot
• Mean, Median, Mode, and Range
• How to Identify an Outlier
• Finding Range, Quartile, and Interquartile Range