Mean, Median, Mode and Range Worksheet and Practice Questions
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Statistics Practice Questions
Build confidence with mean, median, mode, frequency, range, central tendency, grouped data, weighted mean and five-number summary problems. Try each question first, then reveal the answer and explanation.
Practice questions
Open a folder to see every question at that level. Pick an answer to see the explanation straight away. Questions cover the mean, median, mode, range, quartiles, interquartile range, standard deviation, variance, percentile, negative numbers and decimals.
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Beginner
Beginner questions
6 questions
Beginner
Beginner questions
Find the mean of 4, 6, 8 and 10.
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Answer: 7
Explanation: Add the values: 4 + 6 + 8 + 10 = 28. There are 4 values, so 28 ÷ 4 = 7.
Find the median of 3, 7, 9, 12 and 15.
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Answer: 9
Explanation: The values are already in order and there are 5 of them. The third value is in the middle, so the median is 9.
Find the mode of 2, 4, 4, 5 and 7.
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Answer: 4
Explanation: The value 4 appears twice. Every other value appears once, so 4 has the highest frequency and is the mode.
Find the range of -3, 1, 4 and 9.
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Answer: 12
Explanation: The maximum is 9 and the minimum is -3. Range = maximum – minimum = 9 – (-3) = 12.
Find the mean, median and mode of 2, 3, 3, 5 and 7.
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Answer: Mean = 4, Median = 3, Mode = 3
Explanation: The sum is 20, so the mean is 20 ÷ 5 = 4. The middle value is 3, and 3 is also the only value that repeats.
In 1, 2, 2, 3, 3, 3, what is the frequency of 3?
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Answer: 3
Explanation: Count each occurrence of 3. It appears three times, so its frequency is 3.
Intermediate
Intermediate questions
6 questions
Intermediate
Intermediate questions
Find the mean of -5, 0, 5 and 10.
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Answer: 2.5
Explanation: The sum is -5 + 0 + 5 + 10 = 10. Divide by 4 values: 10 ÷ 4 = 2.5.
Find the median of 4, 8, 15, 16, 23 and 42.
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Answer: 15.5
Explanation: There are 6 values, so take the two middle values, 15 and 16. Their average is (15 + 16) ÷ 2 = 15.5.
For 2, 3, 4, 5 and 100, which measure of central tendency better represents a typical value: mean or median?
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Answer: Median
Explanation: The value 100 is much larger than the others and pulls the mean upward. The median is 4, which sits in the center of the ordered data and better represents the typical values.
Scores of 80 (weight 3) and 70 (weight 2) are combined. What is the weighted mean?
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Answer: 76
Explanation: Multiply each score by its weight: 80 × 3 = 240 and 70 × 2 = 140. Then divide 380 by the total weight of 5: 380 ÷ 5 = 76.
A grouped table has classes 10-19 (frequency 2), 20-29 (frequency 3), and 30-39 (frequency 5). Using class midpoints, what is the estimated mean?
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Answer: 27.5
Explanation: The midpoints are 14.5, 24.5 and 34.5. Multiply by the frequencies: 29 + 73.5 + 172.5 = 275. Divide by the total frequency of 10: 275 ÷ 10 = 27.5.
A frequency table shows 5 with frequency 2, 6 with frequency 5, and 7 with frequency 3. What is the mode?
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Answer: 6
Explanation: The highest frequency is 5, and it belongs to the value 6. Therefore, the mode is 6.
Advanced
Advanced questions
6 questions
Advanced
Advanced questions
Find the five-number summary and IQR for 2, 4, 5, 7, 8, 10, 12 and 15.
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Answer: Min = 2, Q1 = 4.5, Median = 7.5, Q3 = 11, Max = 15; IQR = 6.5
Explanation: The two middle values are 7 and 8, so the median is 7.5. The lower half gives Q1 = (4 + 5) ÷ 2 = 4.5. The upper half gives Q3 = (10 + 12) ÷ 2 = 11. Therefore IQR = 11 – 4.5 = 6.5.
Find the weighted mean of 92 (weight 4), 78 (weight 3), and 85 (weight 2).
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Answer: 85.78 approximately
Explanation: The weighted total is 92 × 4 + 78 × 3 + 85 × 2 = 772. The total weight is 9, so 772 ÷ 9 = 85.777…, which rounds to 85.78.
Find the mean, median and mode of 5, 6, 6, 7 and 100. What does the comparison tell you?
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Answer: Mean = 24.8, Median = 6, Mode = 6
Explanation: The sum is 124, so the mean is 24.8. The middle value is 6 and 6 occurs twice. The large value 100 pulls the mean far above the median and mode, showing why more than one measure can be useful.
Find the five-number summary and IQR for -8, -3, 0, 2, 5, 9, 12 and 20.
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Answer: Min = -8, Q1 = -1.5, Median = 3.5, Q3 = 10.5, Max = 20; IQR = 12
Explanation: The median is (2 + 5) ÷ 2 = 3.5. Q1 is (-3 + 0) ÷ 2 = -1.5. Q3 is (9 + 12) ÷ 2 = 10.5. IQR = 10.5 – (-1.5) = 12.
A data set has a strong right-side outlier. Which measure is usually less affected by that outlier: mean or median?
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Answer: Median
Explanation: The mean uses every numerical value, so an unusually large observation can pull it upward. The median depends on position after sorting and is generally less affected by a single extreme value.
Scores are 70 for 5 students, 80 for 3 students, and 90 for 2 students. Find the weighted mean.
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Answer: 77
Explanation: Multiply score by frequency: 70 × 5 = 350, 80 × 3 = 240, and 90 × 2 = 180. The total is 770 across 10 students, so the mean is 770 ÷ 10 = 77.
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