Frequency Tables and Tally Charts
A tally chart is a quick way of recording data as it is collected, using marks grouped in fives, and a frequency table then summarises how many times each value or category occurs. They are the first step in organising raw data before it is displayed in a chart or used to calculate averages, and appear throughout GCSE Statistics as the starting point for processing data.
Method
- List every possible value or category the data could take in the first column of the table.
- Go through the raw data one item at a time and add a tally mark next to the matching category.
- Group tally marks in fives (four vertical strokes with a fifth stroke crossing them) to make counting easier.
- Once all data is tallied, count the tally marks for each row and write the total in a frequency column.
- Check the frequencies add up to the total number of data items collected.
- Use the completed frequency table to find averages, draw charts, or answer questions about the data.
Worked example
The shoe sizes of 20 students, recorded as they are measured, are: 4,5,6,5,7,6,5,4,6,7,5,6,8,5,6,7,5,4,6,5. Draw a frequency table and state the mode.
- List the possible shoe sizes present: 4, 5, 6, 7, 8.
- Count how many times each size appears: size 4 appears 3 times, size 5 appears 7 times, size 6 appears 6 times, size 7 appears 3 times, size 8 appears 1 time.
- Write these counts as the frequency column: 4 -> 3, 5 -> 7, 6 -> 6, 7 -> 3, 8 -> 1.
- Check the frequencies total 3 + 7 + 6 + 3 + 1 = 20, matching the 20 students.
- The mode is the value with the highest frequency, which is size 5 (frequency 7).
Practice questions
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Q1A tally shows 4 full groups of five plus 2 extra marks for one category. What is the frequency?Show answer
Answer: 22 (4 x 5, plus 2)
Q2The frequencies for four categories are 8, 5, 12, 3. What is the total number of data items?Show answer
Answer: 28
Q3A survey of favourite colours gives: Red 6, Blue 9, Green 4, Yellow 5. How many people were surveyed in total?Show answer
Answer: 24
Q4Using the survey in the previous question (Red 6, Blue 9, Green 4, Yellow 5), which colour is the mode?Show answer
Answer: Blue (highest frequency, 9)
Q5The number of pets owned by 15 households, recorded as collected, is: 0,1,2,1,0,3,1,2,0,1,1,2,0,1,2. Complete a frequency table for the number of pets and state the total frequency.Show answer
Answer: 0 -> 4, 1 -> 6, 2 -> 4, 3 -> 1; total = 15
Q6A frequency table for test scores out of 10 shows: score 6 has frequency 5, score 7 has frequency 8, score 8 has frequency x, score 9 has frequency 3, and the total frequency is 25. Find x.Show answer
Answer: 9 (25 minus 5, 8 and 3)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A tally chart uses groups of five marks. One category has 3 full groups of five and then 4 extra single marks. State the frequency for this category, and explain how tally marks make counting large amounts of data easier.
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A researcher records the number of siblings of 24 students as they are asked: 1,0,2,1,3,0,1,2,1,0,2,1,1,0,3,2,1,0,1,2,1,0,1,2. Complete a frequency table and state the number of students with more than 1 sibling.
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The frequency table below shows the number of goals scored by a football team in 20 matches: 0 goals frequency 4, 1 goal frequency 7, 2 goals frequency x, 3 goals frequency 3, 4 goals frequency 1. (a) Find x. (b) State the mode. (c) Find the number of matches in which the team scored at least 2 goals.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
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This topic is chapter 13 of GCSE Statistics Foundation Workbook 1 and chapter 17 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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