How to Solve the Frequency Distribution Table?

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:

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• 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\(\color{blue}{(\text{ xf }) = 2(3)+4(4)+6(2)+8(1) = 6+16+12+8 = 42}\); \(\color{blue}{\text{ Mean } = 42\div 10}\) = 4.2; Mode = 4
3. \(\color{blue}{\text{ Total } = 5+3+2}\) = 10; Σ\(\color{blue}{(\text{ xf }) = 1(5)+2(3)+3(2) = 5+6+6 = 17}\); \(\color{blue}{\text{ Mean } = 17\div 10}\) = 1.7
4. B and C are both modes (both have frequency 7; this is bimodal)
5. Σ\(\color{blue}{(\text{ xf }) = 70(3)+80(5)+90(2) = 210+400+180 = 790}\); \(\color{blue}{\text{ Mean } = 790\div 10}\) = 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 the difference between a frequency table and a tally chart?

A tally chart uses tally marks (lines) to count while the data is being collected. A frequency table replaces those tally marks with numbers. Both show the same information; the frequency table is the organized, final version.

Can I find the median from a frequency table?

Yes. Add the frequencies cumulatively and find the value where the cumulative frequency reaches the middle of the total count. For a total of n, the median is at position \(\color{blue}{\frac{(n+1)}{2}}\).

What is relative frequency?

Relative \(\color{blue}{\text{ frequency } = (\text{ frequency of a value }) \div (\text{ total frequency })}\). It shows the proportion (or percentage) of the data that falls at each value. All relative frequencies in a table must sum to 1 (or 100%).

Related Topics

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