Analysing frequency tables
When you're looking at a big set of data – like test scores or survey results – it's not always easy to make sense of all the numbers. That’s where mean, median, mode, and range come in. These are ways to summarise the data and spot patterns. And when the data is organised in a frequency table, it helps you quickly see what happens most often, what's typical, and how spread out the results are – skills that come in handy in everything from science experiments to sports stats! Jump to the questions
Practise now
Calculate the mode, range, mean, and median.
Topic guide
What this worksheet practises
This worksheet practises extracting and analysing data from frequency tables. Frequency tables summarise large sets of data by showing how often each value occurs. You will need to use these tables to find key statistical measures such as the mode, median, mean, and range.
Key method
To find averages from a frequency table, you must remember that the frequency column tells you how many of each value there are.
- Mode: Look for the highest number in the frequency column. The mode is the corresponding value, not the frequency itself.
- Median: Add up the frequencies to find the total number of values (n). The median is the (n + 1) ÷ 2 th value. Count through the frequencies until you reach this position.
- Mean: Add a third column to your table where you multiply the value by its frequency (Value × Frequency). Sum this new column to find the total sum of all values, then divide by the total frequency.
Worked example
Find the mean number of goals scored from the table:
- 0 goals: frequency of 2
- 1 goal: frequency of 4
- 2 goals: frequency of 3
Step 1: Multiply Goals by Frequency to get the total goals for each row.
- 0 × 2 = 0
- 1 × 4 = 4
- 2 × 3 = 6
Step 2: Find the total number of goals (0 + 4 + 6 = 10) and the total frequency (2 + 4 + 3 = 9).
Step 3: Divide the total goals by the total frequency.
10 ÷ 9 = 1.11 (to 2 decimal places).
The mean number of goals is 1.11.
Common mistakes to avoid
When finding the mean, a very common mistake is dividing the total sum by the number of rows in the table, rather than dividing by the total frequency. Always ensure you divide by the sum of the frequency column.