Graphs, data and probability
Mean, median and mode: calculate and compare
Learn how mean, median and mode describe a data set, and how an added value changes them. Six practice questions include full calculations.
Grades 6–7 practice · 6 questions · Free to print · Answers included
Make sense of the method
Mean shares the total equally. Median is the middle of an ordered list. Mode is the most frequent value; there may be no mode or more than one.
These summaries answer different questions. An unusually large value can move the mean much more than the median. Keep the original data visible when interpreting a summary.
- Copy every observation, including repeated values, and put the data in order.
- For the mean, add all observations and divide by how many there are.
- For the median, find the middle value; with an even count, average the two middle values.
- Count each value's frequency to find the mode, then explain the result in the original units.
A worked example
Five mini-puzzles took 3, 5, 5, 7 and 10 minutes. Find the mean, median and mode.
- The total is 3 + 5 + 5 + 7 + 10 = 30 minutes.
- Mean = 30 ÷ 5 = 6 minutes.
- The ordered list has five entries, so its third entry, 5, is the median.
- 5 appears twice; every other value appears once. The mode is 5.
Mean 6 minutes; median 5 minutes; mode 5 minutes.
Try the worksheet
Start with the first two questions, then build toward the final challenge. Show your method with calculations, drawings or a short explanation. These are practice questions with published answers, not a full-topic readiness check.
Build the foundation
1.An invented list of four reading-session lengths is 7, 5, 9, 3 minutes. Put it in order and find the median. Show why you use two middle values.
Show your work on paper.Build the foundation
2.Five paper towers have heights 8, 10, 6, 12, 9 cm. Calculate their mean, showing the total and divisor.
Show your work on paper.Strengthen your method
3.An invented list of daily badge counts is 2, 4, 2, 6, 4, 7. Find every mode and the median. Explain why there is more than one mode.
Show your work on paper.Strengthen your method
4.Four practice times are 4, 6, 8, 10 minutes. Add a fifth time of 32 minutes. Find the mean and median before and after, then compare their changes.
Show your work on paper.Apply and explain
5.Five quiz-practice scores have a mean of 14 points. Four scores are 11, 13, 16 and 12 points. Find the missing score and check the mean.
Show your work on paper.Apply and explain
6.Five invented weekend screen-time records are 20, 25, 25, 30, 150 minutes. Calculate mean, median and mode. Which of the mean or median better describes the cluster of shorter records here? Explain without deleting the 150-minute record.
Show your work on paper.
Worked answers
Try the questions first. Then compare the reasoning, not just the final result.
Show all six worked solutions
1. Ordered: 3, 5, 7, 9. Median: 6 minutes.
- Arrange the four observations: 3, 5, 7, 9.
- An even count has two middle observations, 5 and 7.
- Median = (5 + 7) ÷ 2 = 6 minutes; it need not be an observed value.
2. 9 cm.
- Total height = 8 + 10 + 6 + 12 + 9 = 45 cm.
- There are five towers, so mean = 45 ÷ 5 = 9 cm.
3. Modes: 2 and 4. Median: 4.
- Ordered list: 2, 2, 4, 4, 6, 7.
- 2 and 4 each occur twice, tying for highest frequency; both are modes.
- The middle observations are 4 and 4, giving (4 + 4) ÷ 2 = 4.
4. Before: mean 7, median 7. After: mean 12, median 8. The mean rises by 5 minutes; the median rises by 1 minute.
- Before: total 28, mean 28/4 = 7; median (6 + 8)/2 = 7.
- After: ordered list 4, 6, 8, 10, 32; total 60, mean 60/5 = 12.
- The new middle observation is 8. Changes are 12 − 7 = 5 and 8 − 7 = 1 minute.
- The large new value affects the total strongly but does not become the middle observation.
5. 18 points.
- Mean × count gives total: 14 × 5 = 70 points.
- Known total = 11 + 13 + 16 + 12 = 52.
- Missing score = 70 − 52 = 18. Check: (52 + 18) ÷ 5 = 14.
6. Mean 50 minutes; median 25 minutes; mode 25 minutes. The median better describes the cluster from 20 to 30 minutes.
- Total = 20 + 25 + 25 + 30 + 150 = 250; mean = 250/5 = 50 minutes.
- The middle observation is 25. It also occurs most often, so median and mode are both 25.
- Four records lie between 20 and 30; the median describes that cluster better. The mean still correctly represents the total shared equally, including 150.
- Report the unusually large record rather than silently removing it.
Mistakes worth catching
Finding the middle before sorting.
Order all observations, retaining repetitions.
Dividing by the number of different values.
Count every observation, including duplicates.
Assuming the mode is unique.
Check frequencies; ties can produce multiple modes.
Turn your work into a next step
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Skills covered
Graphs, data and probability
- Calculate mean, median and mode and explain their differences.
- Investigate how changing a data set affects its summaries.
Choose this practice by the skills you need. Grade placement and strand names vary between school systems; one worksheet covers selected skills rather than every expectation in a topic.
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