IGCSE Mathematics: Averages and Range Practice Questions
The mean is the total divided by how many values there are, the median is the middle value once the data is ordered, and the mode is the most common value. The range is the largest value minus the smallest.
Topic 9.2 of Cambridge IGCSE Mathematics 0580 appears in every statistics question that follows. The two versions worth practising hardest are the mean from a frequency table and the estimated mean from grouped data, because both use the same sum of fx method. The questions below build to that.
What you need to know for Averages and Range
- MeanAdd all the values and divide by how many there are. It uses every value, so it is affected by extreme values.
- MedianOrder the data, then take the middle value. With an even number of values, take the mean of the two middle ones.
- ModeThe value occurring most often. A data set can have more than one mode, or none at all.
- RangeLargest value minus smallest value. It measures spread, not average.
- Mean from a frequency tableMultiply each value by its frequency, add those products to get the sum of fx, then divide by the total frequency.
- Estimated mean from grouped dataUse the midpoint of each class as the value, then apply the same method. It is an estimate because the exact values within each class are unknown.
IGCSE Mathematics Averages and Range questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
Find the mean, median, mode and range of the data 4, 7, 7, 9, 13.
Show the worked answer
- Mean: add the values, 4 + 7 + 7 + 9 + 13 = 40, then divide by 5 to get 8.
- Median: the data is already ordered and there are 5 values, so the middle one is the third, which is 7.
- Mode: 7 appears twice and every other value once, so the mode is 7.
- Range: 13 minus 4 = 9.
The mean of five numbers is 12. Four of them are 8, 11, 14 and 15. Calculate the fifth number.
Show the worked answer
- The mean is the total divided by the count, so the total is the mean multiplied by the count.
- Total of all five numbers = 12 x 5 = 60.
- Sum of the four known numbers = 8 + 11 + 14 + 15 = 48.
- The fifth number = 60 minus 48 = 12.
A frequency table shows: 0 goals scored in 4 matches, 1 goal in 7 matches, 2 goals in 6 matches and 3 goals in 3 matches. Calculate the mean number of goals per match.
Show the worked answer
- Multiply each value by its frequency: 0 x 4 = 0, 1 x 7 = 7, 2 x 6 = 12, 3 x 3 = 9.
- Add these products to find the sum of fx: 0 + 7 + 12 + 9 = 28 goals in total.
- Add the frequencies to find the number of matches: 4 + 7 + 6 + 3 = 20.
- Mean = 28 divided by 20 = 1.4 goals per match.
Times taken to complete a task are grouped as 0 to 10 minutes (5 people), 10 to 20 minutes (12 people) and 20 to 30 minutes (3 people). Calculate an estimate of the mean time, and explain why it is only an estimate.
Show the worked answer
- Use the midpoint of each class as the representative value: 5, 15 and 25 minutes.
- Multiply each midpoint by its frequency: 5 x 5 = 25, 15 x 12 = 180, 25 x 3 = 75.
- Sum of fx = 25 + 180 + 75 = 280. Total frequency = 5 + 12 + 3 = 20.
- Estimated mean = 280 divided by 20 = 14 minutes.
- It is only an estimate because the original data has been grouped, so the individual times are not known. Assuming every value sits at the midpoint of its class introduces error.
Common mistakes in this topic
- Finding a median without ordering the data.
- Dividing by the number of table rows instead of the total frequency.
- Using class boundaries rather than midpoints for grouped data.
- Confusing range with mean, or calling the range an average.
- Presenting an estimated mean as an exact value.
Exam tips
- Add an fx column to any frequency table before calculating. It structures the working and earns method marks.
- The divisor is always the total frequency, so add the frequency column too.
- For grouped data, write the midpoints in first and label them clearly.
- For a missing value question, reconstruct the total from the mean and the count.
- State that a grouped mean is an estimate. That word alone is sometimes worth a mark.
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Averages and Range FAQs
How do I calculate the mean from a frequency table?
Multiply each value by its frequency, add those products to get the sum of fx, then divide by the total frequency. The divisor is the sum of the frequency column, not the number of rows in the table.
How do I estimate the mean from grouped data?
Use the midpoint of each class as the representative value, multiply each midpoint by its frequency, add the products, and divide by the total frequency. The result is an estimate because the individual values within each class are unknown.
Why is a grouped mean only an estimate?
Once data is grouped, the individual values are lost. Assuming every value sits exactly at the midpoint of its class introduces error, since the real values are spread across the class. The calculated figure is therefore an estimate rather than the true mean.
What is the difference between mean, median and mode?
The mean is the total divided by the number of values and uses every value, so extreme values affect it. The median is the middle value when ordered and is unaffected by extremes. The mode is the most frequently occurring value and is the only average usable for categorical data.
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.