The number of pets owned by 30 people:
- Work out the mean number of pets.[3]
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A frequency table records how often each value, or each group of values, occurs. It saves writing out long lists — but it also changes how you find averages. With grouped data the exact values are lost, so the mean can only be using class midpoints.
The big picture
A frequency of 6 next to the value 3 means "3, 3, 3, 3, 3, 3". So the total of all the values is found by multiplying each value by its frequency and adding: . The mean is then .
For grouped data such as , you do not know where each value lies within its class, so you assume they sit at the midpoint. That is why the answer is an estimate — and why the question always says "estimate".
What you'll learn
Mode: the value with the highest frequency. Median: find the position and count through the frequencies to reach it. Mean: add an column, then divide by .
Scores on a quiz: score 1 (frequency 3), score 2 (frequency 7), score 3 (frequency 6), score 4 (frequency 4). Find the mean score.
Tip — The mean is — dividing by the number of rows is the most common error.
The has the highest frequency. The class containing the median is found by counting cumulative frequencies to position (for large data sets).
To estimate the mean: find the midpoint of each class, multiply by the frequency, add, and divide by the total frequency.
Masses: (frequency 5), (frequency 8), (frequency 7). Estimate the mean mass.
The estimate is only as good as the midpoint assumption. If most runners in actually finished close to 26 minutes, the true mean would be lower than 30. That is why "explain why your answer is an estimate" is a common one-mark question: "the exact values are not known; midpoints were used".
A two-way table shows two categories at once. Row and column totals let you fill in missing cells by subtraction.
In a club of 45 members, 25 are adults. 18 members swim, and 11 of the swimmers are children. How many adults do not swim?
Think like an examiner
From frequency tables
Watch out for these
Stretch yourself
A frequency table has values 1, 2, 3 and 4 with frequencies 5, , 8 and 2. The mean is 2.2. Find .
Hint — Write and in terms of , then set up .
Questions students ask
Key takeaways
Exam-style questions
2 original questions · 7 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.
The number of pets owned by 30 people:
Heights of 50 plants (cm):
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Real past-paper questions on Frequency Tables, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.