Frequency Table Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Frequency Table.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

A frequency table is a table that records how often each value or category occurs in a data set, organizing raw data into a clear summary with categories in one column and their counts (frequencies) in another.

A frequency table is an organized list that answers 'how many?' for each category. Instead of a messy list of responses, you get a clean summary: Pizza-12, Tacos-8, Burgers-5.

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How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Frequency Table organizes data so the right pattern is visible without distorting the counts or scale.

Common stuck point: Students often know a procedure related to frequency table but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?

Worked Examples

Example 1

medium
A frequency table has 5 categories with frequencies 6, 9, 4, 8, yy. The total is 35. Find yy.

Answer

88

First step

1
Known sum =6+9+4+8=27= 6 + 9 + 4 + 8 = 27.

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Example 2

hard
A class of 25 records favorite season. Winter 6, Spring ss, Summer s+2s+2, Fall 4. Find ss.

Example 3

medium
A class of 40 records favorite drink. Tea 8, water 14, juice 12, milk mm. Find mm, then state the modal drink's frequency.

Example 4

challenge
Two frequency tables from different classes both have total 30. Class A's modal category has frequency 14; Class B's has 12. If we combine the two classes, what is the largest possible frequency for any single category in the combined table?

Example 5

easy
Students were asked how many siblings they have: 0, 1, 2, 1, 3, 1, 0, 2, 1, 1, 2, 0, 1, 3, 2. Create a frequency table and find the most common number of siblings.

Example 6

medium
A frequency table shows test scores in intervals: 50–59 (3), 60–69 (7), 70–79 (10), 80–89 (5), 90–99 (2). Find the total number of students and identify the modal class.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A frequency table shows counts 5, 8, 3, 4. What is the total frequency?

Example 2

easy
In a frequency table, 'blue' has frequency 7. How many times did blue occur?

Example 3

easy
A frequency table has categories with counts 2, 2, 2, 2, 2. What is the total?

Example 4

easy
Which category is most frequent if counts are A:4, B:9, C:6? Answer with the highest frequency.

Example 5

easy
A frequency table lists frequencies 6 and 9 for two categories. How many more in the larger?

Example 6

easy
A frequency table covers 3 categories with total 18 split equally. What is each frequency?

Example 7

easy
A frequency table shows 4, 0, 7, 5. What is the total frequency?

Example 8

easy
If 'cat' has frequency 5 and 'dog' has frequency 8, how many pets in those two categories?

Example 9

medium
A frequency table has counts 12, 9, x, 4 with total 30. What is x?

Example 10

medium
A frequency table of 40 responses shows 'yes' with frequency 24. What fraction said yes? Give a simplified fraction.

Example 11

medium
A frequency table shows 5, 10, 15, 10. What is the mean frequency across the 4 categories?

Example 12

medium
A frequency table of 50 shows 'A' with frequency 20. What percent is category A?

Example 13

medium
Two frequency tables both total 25; the first has a max category of 11, the second a max of 9. What is the difference in their largest categories?

Example 14

medium
A frequency table records 3 categories where the second is double the first and the third equals the first. If the first is 6, what is the total?

Example 15

challenge
A frequency table of 60 has categories in proportions 1/2, 1/3, and the rest. How many are in the 'rest' category?

Example 16

challenge
A frequency table has counts a, a+2, a+4 summing to 30. What is the largest frequency?

Example 17

challenge
A frequency table of 80 shows category X with relative frequency 0.35. How many fall in category X?

Example 18

medium
A frequency table has counts 7, 11, x, 6 with total 30. What is x?

Example 19

medium
A frequency table of 80 shows 'A' with frequency 32. What percent is A?

Example 20

medium
A frequency table shows 8, 8, 8, 8, 8. What is the total?

Example 21

easy
A frequency table shows counts 7, 9, 4, 6, 2. What is the total frequency?

Example 22

easy
In a frequency table, 'green' has frequency 11. How many times did green occur?

Example 23

easy
A frequency table has 6 categories all with frequency 4. What is the total?

Example 24

easy
A frequency table lists 12 and 5 for two categories. How many more does the larger have?

Example 25

easy
A frequency table covers 4 categories with total 32 split equally. What is each frequency?

Example 26

easy
A frequency table shows 0, 3, 6, 9. What is the total frequency?

Example 27

easy
If 'rain' has frequency 9 and 'sun' has frequency 12, how many days fall in those two weather categories?

Example 28

medium
A frequency table has counts 14, 8, xx, 11 with total 45. Find xx.

Example 29

medium
A frequency table of 60 responses shows 'no' with frequency 36. What fraction said no? Give simplified.

Example 30

medium
A frequency table shows 8, 14, 11, 7. What is the mean frequency across the 4 categories?

Example 31

medium
A frequency table shows tally marks for vowels: a=12, e=18, i=8, o=15, u=7. What is the modal vowel's frequency?

Example 32

medium
A frequency table of 24 shows 'A' frequency 6. What fraction of the total is A? Simplify.

Example 33

medium
A frequency table for 50 students shows reading 18, gaming 16, sports 9, art aa. Find aa.

Example 34

hard
A frequency table has 4 categories. The frequencies are in ratio 1:2:3:41:2:3:4 with total 60. What is the largest frequency?

Example 35

hard
A frequency table of 200 shows the mode 'X' with frequency 80. What is the relative frequency of X as a decimal?

Example 36

hard
A relative frequency table sums to 1 across categories 0.20, 0.15, 0.30, rr. Find rr.

Example 37

medium
A frequency table shows boys 18 and girls 22 prefer outdoor recess. What fraction prefer outdoor that are boys? Simplify.

Example 38

challenge
A frequency table of 100 has 5 categories. The largest frequency is twice the smallest, and the three middle frequencies are 18, 20, 22. If the largest is LL and smallest is SS with L=2SL = 2S and L+S=40L + S = 40, find LL.

Example 39

easy
Dice rolls: 3, 5, 2, 6, 3, 1, 4, 3, 5, 2, 6, 3, 4, 1, 5. Create a frequency table for values 1 through 6.

Example 40

easy
Favourite pets are: Cat, Dog, Dog, Fish, Cat, Dog, Bird, Cat, Fish, Dog, Cat. Create a frequency table and state how many responses were recorded.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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