Frequency Charts: How to Understanding Trends

How to frequency charts: how to understanding trends, 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.

Frequency charts are one of the most practical tools in statistics. Once you know how to read them, you can quickly spot patterns, compare groups, and describe data using numbers. On the GED Math test, you may be asked to build a frequency table, calculate relative frequencies, or identify a trend in a chart. This lesson explains everything step by step.

What Is a Frequency Chart?

A frequency chart (also called a frequency table) organizes data by listing each category or value alongside the number of times it appears. Its frequency. When the counts are converted to fractions or percentages of the whole, they become relative frequencies. Frequency charts make it easy to see which category is most or least common and to track trends across groups.

How to Read and Build a Frequency Chart

1. List the categories

Write each possible value or category in the first column. In a survey of 10 students’ favorite sports the categories might be Soccer, Basketball, Tennis, and Swimming.

2. Count the tally and record the frequency

Go through the data one item at a time, add a tally mark, then write the total count in the Frequency column.

3. Compute relative frequency

Divide each frequency by the total count: Relative \(\color{blue}{\text{ Frequency } = \text{ Frequency } \div \text{ Total }}\). Multiply by 100 to get a percentage.

4. Identify trends

Look for the category with the highest (or lowest) frequency. In a time-series chart, look for whether frequencies increase, decrease, or stay roughly constant across intervals.

Example frequency table (n = 10 students):

Step-by-Step Summary

1. List every category in the first column.
2. Count how many times each category appears and record the frequency.
3. Add all frequencies to find the total.
4. Divide each frequency by the total to get the relative frequency.
5. Multiply by 100 to convert to a percentage.
6. Scan the chart: the highest \(\color{blue}{\text{ frequency } = \text{ the }}\) mode; compare percentages to spot trends.

Watch: Frequency Tables and Dot Plots (Khan Academy)

This Khan Academy video shows how to build frequency tables and connect them to dot plots, a great visual companion to the steps above:

Worked Examples

Example 1: A class of 20 students was asked their favorite color. The results were: Blue 8, Red 5, Green 4, Yellow 3. What is the relative frequency of Blue?

Relative \(\color{blue}{\text{ frequency } = 8 \div 20}\) = 0.40 (or 40%). Blue is the most popular color.

Example 2: Using the data above, what percentage of students prefer Red or Green?

\(\color{blue}{\text{ Red } + \text{ Green } = 5 + 4 = 9}\) students. \(\color{blue}{\text{ Percentage } = 9 \div 20 \times 100}\) = 45%.

Example 3: A frequency chart for weekly sales shows Monday 12, Tuesday 15, Wednesday 18, Thursday 22, Friday 28. Describe the trend.

Sales increase each day from Monday to Friday, a clear upward trend. Friday sales (28) are more than double Monday sales (12).

Example 4: In a frequency table showing test scores, the score 85 appears 6 times out of 30 total scores. What is its relative frequency?

Relative \(\color{blue}{\text{ frequency } = 6 \div 30}\) = 0.20 (20%).

More Practice: Reading a Frequency Table (Math with Mr. J)

Math with Mr. J walks through qualitative frequency tables with clear visuals and relatable examples:

Exercises

Use the frequency table skills above to answer each question.

1. A survey of 25 people shows: Dogs 10, Cats 8, Fish 4, Birds 3. What is the relative frequency of Cats?
2. Using the same table, what percentage prefer Dogs or Cats combined?
3. A store tracks daily visitors: Mon 45, Tue 52, Wed 48, Thu 61, Fri 70. Which day had the highest frequency?
4. Out of 50 survey responses, 15 chose “Strongly Agree.” What is the relative frequency?
5. In a chart where total \(\color{blue}{\text{ frequency } = 40}\) and the relative frequency of one category is 0.25, how many people are in that category?
6. A frequency table has three categories with frequencies 12, 18, and 10. What is the total, and what percent does the category with 18 represent?

Answers

1. \(\color{blue}{8 \div 25}\) = 0.32 (32%)
2. \(\color{blue}{(10 + 8) \div 25 \times 100}\) = 72%
3. Friday (70 visitors)
4. \(\color{blue}{15 \div 50}\) = 0.30 (30%)
5. \(\color{blue}{0.25 \times 40}\) = 10 people
6. \(\color{blue}{\text{ Total } = 12 + 18 + 10 = 40}\); \(\color{blue}{18 \div 40 \times 100}\) = 45%

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Frequently Asked Questions

What is a frequency chart?

A frequency chart, also called a frequency table, lists each category or value next to how many times it occurs. If 20 students name their favorite fruit and 8 say apples, 5 bananas, 4 grapes, and 3 oranges, those counts are the frequencies, and they add up to 20. Seeing the counts side by side makes the most and least popular choices obvious at a glance.

How do you make a frequency chart?

List every possible category or value in the first column. Go through the raw data one item at a time and make a tally mark beside the matching category, grouping tallies in fives. Then write each total in a frequency column and check that the totals add up to the number of data items. A relative frequency column, frequency ÷ total, lets you compare categories as percentages.

How do you find the mean from a frequency table?

Multiply each value by its frequency, add the products, and divide by the total frequency. Suppose a class records pets owned: 0 pets (4 students), 1 pet (7), 2 pets (6), 3 pets (3). The products are 0, 7, 12, and 9, which sum to 28. There are 20 students, so the mean is 28 ÷ 20 = 1.4 pets. Dividing by the number of rows instead is a common mistake.

How do you find the median from a frequency table?

Add a running total of the frequencies to locate the middle position. For shoe sizes 6 (3 people), 7 (5), 8 (8), and 9 (4), there are 20 values, so the median is the average of the 10th and 11th. The running totals are 3, 8, 16, and 20. Positions 9 through 16 are all size 8, so the median is 8.

How do you read a frequency table?

Read the headings first so you know what each value and count means, then scan the frequency column. The largest frequency shows the most common category, the mode, and the smallest shows the rarest. To spot a trend, compare frequencies across categories or time periods, for example sales rising from 12 to 18 to 25 over three months. Converting to percentages helps when two tables have different totals.

What is the difference between tally charts and frequency tables?

A tally chart records counts with tally marks as you collect data, while a frequency table shows those counts as numbers. Many charts include both columns side by side, so one bundle of five tallies plus two more marks becomes a frequency of 7. Tallies are handy during a survey because you add one mark at a time, and the numbers are easier for totals, means, and percentages.

Related Topics

• How to Solve the Frequency Distribution Table
• Distributions in Line Plot
• How to Interpret Categorical Data
• Finding Mean, Median, Mode and Range: Interpreting Charts
• Line Plot