Grouped Frequency Tables
A grouped frequency table organises continuous or wide-ranging numerical data into class intervals, recording how many data values fall into each group rather than listing every individual value. It is used when there are too many different values to list separately, and is the basis for drawing histograms and estimating averages such as the estimated mean.
Before you start
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Method
- Look at the range of the raw data and choose suitable, equal-width class intervals that cover every value with no gaps or overlaps.
- Write the class intervals in the first column, usually using inequality notation such as 10 <= x < 20.
- Go through the raw data and tally each value into the class interval it belongs to.
- Count the tallies for each class interval to get the frequency, and write it in the frequency column.
- Check the frequencies add up to the total number of data values collected.
- Use the table to estimate the mean, draw a histogram, or find the modal class and the class containing the median.
Worked example
The ages, in years, of 15 people at a gym are: 22, 35, 41, 19, 28, 33, 45, 24, 30, 38, 27, 42, 20, 36, 31. Group this data into class intervals of width 10, starting at 15.
- Choose class intervals of width 10 covering the data: 15 <= x < 25, 25 <= x < 35, 35 <= x < 45, 45 <= x < 55.
- Sort each value into the interval it fits: 22, 19, 24, 20 fall into 15 <= x < 25 (4 values).
- 28, 33, 30, 27, 31 fall into 25 <= x < 35 (5 values).
- 35, 41, 38, 42, 36 fall into 35 <= x < 45 (5 values).
- 45 falls into 45 <= x < 55 (1 value), since it is not less than 45.
Practice questions
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Q1A class interval is written 10 <= x < 20. Which of these values belong in it: 10, 20, 15?Show answer
Answer: 10 and 15 (20 belongs to the next interval)
Q2The frequencies for four class intervals are 6, 9, 11, 4. Find the total number of data values.Show answer
Answer: 30
Q3Values of 12, 18, 25, 31, 9, 22, 15 are grouped using intervals 0 <= x < 10, 10 <= x < 20, 20 <= x < 30, 30 <= x < 40. State the frequency of the interval 10 <= x < 20.Show answer
Answer: 3 (values 12, 18 and 15)
Q4Using the data in the previous question (12, 18, 25, 31, 9, 22, 15), state the frequency of the interval 20 <= x < 30.Show answer
Answer: 2 (values 25 and 22)
Q5Why must class intervals in a grouped frequency table not overlap?Show answer
Answer: So that every data value belongs to exactly one interval and is not counted twice.
Q6A grouped frequency table has intervals of unequal width, 0 <= x < 10 and 10 <= x < 40. Explain why this could make the table misleading when drawing a histogram.Show answer
Answer: Frequency alone no longer fairly represents how densely packed the data is, since the wider interval can appear to contain disproportionately more data unless frequency density is used.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
Explain why raw data with a very wide range of values, such as annual salaries from 15000 pounds to 95000 pounds, is usually grouped before being displayed in a frequency table.
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The times, in minutes, taken by 20 runners to finish a race are grouped as follows: 20 <= t < 30 frequency 5, 30 <= t < 40 frequency 8, 40 <= t < 50 frequency x, 50 <= t < 60 frequency 2. (a) Find x. (b) State the modal class.
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A gym records the weights, in kg, lifted by 24 members, grouped as: 40 <= w < 55 frequency 6, 55 <= w < 70 frequency 10, 70 <= w < 85 frequency y, 85 <= w < 100 frequency 3. (a) Find y. (b) Write down the class interval that contains the median. (c) Explain why you cannot find the exact median from a grouped frequency table.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the grouped frequency tables worksheet pack - 16 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 14 of GCSE Statistics Foundation Workbook 1 and chapter 18 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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