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Home / Practice / Maths
Mean, median, mode and range, and working backwards from an average to a missing value.
Question 1 of 12
Here are seven numbers: 11, 14, 1, 15, 14, 14, 20. What is the median?
Put them in order first, whichever is being asked for: 1, 11, 14, 14, 14, 15, 20. The median is the middle one. With seven numbers the middle is the fourth, which is 14. Finding the middle of the unsorted list is the mistake to avoid. Median is the middle, mode is the most common, range is the spread. Mode and most both start with m.
The answer is B. Put them in order first, whichever is being asked for: 1, 11, 14, 14, 14, 15, 20. The median is the middle one. With seven numbers the middle is the fourth, which is 14. Finding the middle of the unsorted list is the mistake to avoid. Median is the middle, mode is the most common, range is the spread. Mode and most both start with m.
Find the mean of these numbers: 29, 26, 24, 33.
The mean is the total shared out equally. Add them up: 29 + 26 + 24 + 33 = 112. There are 4 numbers, so divide by 4: 112 ÷ 4 = 28. The mean should sit somewhere between the smallest (24) and the largest (33), which 28 does — a quick check worth making every time. The mean always lies between the smallest and largest value. If yours does not, check the addition.
The answer is C. The mean is the total shared out equally. Add them up: 29 + 26 + 24 + 33 = 112. There are 4 numbers, so divide by 4: 112 ÷ 4 = 28. The mean should sit somewhere between the smallest (24) and the largest (33), which 28 does — a quick check worth making every time. The mean always lies between the smallest and largest value. If yours does not, check the addition.
In 5 spelling tests, the mean score was 16. The first 4 scores were 8, 2, 16, 14. What was the last score?
Work backwards from the mean to the total. If 5 scores have a mean of 16, the total must be 16 × 5 = 80. The scores already known add to 8 + 2 + 16 + 14 = 40. The last one is the difference: 80 − 40 = 40. Going from the mean back to the total is the move this question is really testing. Check by finding the mean of all the numbers including your answer. It should come back to what you were told.
The answer is A. Work backwards from the mean to the total. If 5 scores have a mean of 16, the total must be 16 × 5 = 80. The scores already known add to 8 + 2 + 16 + 14 = 40. The last one is the difference: 80 − 40 = 40. Going from the mean back to the total is the move this question is really testing. Check by finding the mean of all the numbers including your answer. It should come back to what you were told.
Find the mean of these numbers: 31, 31, 32, 10.
The mean is the total shared out equally. Add them up: 31 + 31 + 32 + 10 = 104. There are 4 numbers, so divide by 4: 104 ÷ 4 = 26. The mean should sit somewhere between the smallest (10) and the largest (32), which 26 does — a quick check worth making every time. Add them all, divide by how many there are. Counting how many is the step that gets rushed.
The answer is D. The mean is the total shared out equally. Add them up: 31 + 31 + 32 + 10 = 104. There are 4 numbers, so divide by 4: 104 ÷ 4 = 26. The mean should sit somewhere between the smallest (10) and the largest (32), which 26 does — a quick check worth making every time. Add them all, divide by how many there are. Counting how many is the step that gets rushed.
Here are seven numbers: 2, 10, 4, 8, 7, 4, 16. What is the range?
Put them in order first, whichever is being asked for: 2, 4, 4, 7, 8, 10, 16. The range is the spread: largest minus smallest. 16 − 2 = 14. The range is not an average at all — it describes how spread out the numbers are. Median is the middle, mode is the most common, range is the spread. Mode and most both start with m.
The answer is B. Put them in order first, whichever is being asked for: 2, 4, 4, 7, 8, 10, 16. The range is the spread: largest minus smallest. 16 − 2 = 14. The range is not an average at all — it describes how spread out the numbers are. Median is the middle, mode is the most common, range is the spread. Mode and most both start with m.
Here are seven numbers: 16, 16, 14, 4, 10, 15, 16. What is the range?
Put them in order first, whichever is being asked for: 4, 10, 14, 15, 16, 16, 16. The range is the spread: largest minus smallest. 16 − 4 = 12. The range is not an average at all — it describes how spread out the numbers are. Order the numbers before anything else. Median and range both depend on it, and mode is easier to see too.
The answer is B. Put them in order first, whichever is being asked for: 4, 10, 14, 15, 16, 16, 16. The range is the spread: largest minus smallest. 16 − 4 = 12. The range is not an average at all — it describes how spread out the numbers are. Order the numbers before anything else. Median and range both depend on it, and mode is easier to see too.
In 5 spelling tests, the mean score was 13. The first 4 scores were 9, 24, 3, 7. What was the last score?
Work backwards from the mean to the total. If 5 scores have a mean of 13, the total must be 13 × 5 = 65. The scores already known add to 9 + 24 + 3 + 7 = 43. The last one is the difference: 65 − 43 = 22. Going from the mean back to the total is the move this question is really testing. Mean times how many gives the total. That one reversal unlocks every missing-value question.
The answer is B. Work backwards from the mean to the total. If 5 scores have a mean of 13, the total must be 13 × 5 = 65. The scores already known add to 9 + 24 + 3 + 7 = 43. The last one is the difference: 65 − 43 = 22. Going from the mean back to the total is the move this question is really testing. Mean times how many gives the total. That one reversal unlocks every missing-value question.
Find the mean of these numbers: 25, 19, 23, 13.
The mean is the total shared out equally. Add them up: 25 + 19 + 23 + 13 = 80. There are 4 numbers, so divide by 4: 80 ÷ 4 = 20. The mean should sit somewhere between the smallest (13) and the largest (25), which 20 does — a quick check worth making every time. Add them all, divide by how many there are. Counting how many is the step that gets rushed.
The answer is C. The mean is the total shared out equally. Add them up: 25 + 19 + 23 + 13 = 80. There are 4 numbers, so divide by 4: 80 ÷ 4 = 20. The mean should sit somewhere between the smallest (13) and the largest (25), which 20 does — a quick check worth making every time. Add them all, divide by how many there are. Counting how many is the step that gets rushed.
Here are seven numbers: 20, 2, 11, 7, 9, 14, 9. What is the range?
Put them in order first, whichever is being asked for: 2, 7, 9, 9, 11, 14, 20. The range is the spread: largest minus smallest. 20 − 2 = 18. The range is not an average at all — it describes how spread out the numbers are. With an even number of values the median is halfway between the middle two.
The answer is D. Put them in order first, whichever is being asked for: 2, 7, 9, 9, 11, 14, 20. The range is the spread: largest minus smallest. 20 − 2 = 18. The range is not an average at all — it describes how spread out the numbers are. With an even number of values the median is halfway between the middle two.
In 5 weeks of a reading challenge, the mean score was 20. The first 4 scores were 9, 28, 19, 38. What was the last score?
Work backwards from the mean to the total. If 5 scores have a mean of 20, the total must be 20 × 5 = 100. The scores already known add to 9 + 28 + 19 + 38 = 94. The last one is the difference: 100 − 94 = 6. Going from the mean back to the total is the move this question is really testing. Mean times how many gives the total. That one reversal unlocks every missing-value question.
The answer is B. Work backwards from the mean to the total. If 5 scores have a mean of 20, the total must be 20 × 5 = 100. The scores already known add to 9 + 28 + 19 + 38 = 94. The last one is the difference: 100 − 94 = 6. Going from the mean back to the total is the move this question is really testing. Mean times how many gives the total. That one reversal unlocks every missing-value question.
In 5 weeks of a reading challenge, the mean score was 23. The first 4 scores were 32, 34, 14, 22. What was the last score?
Work backwards from the mean to the total. If 5 scores have a mean of 23, the total must be 23 × 5 = 115. The scores already known add to 32 + 34 + 14 + 22 = 102. The last one is the difference: 115 − 102 = 13. Going from the mean back to the total is the move this question is really testing. Mean times how many gives the total. That one reversal unlocks every missing-value question.
The answer is A. Work backwards from the mean to the total. If 5 scores have a mean of 23, the total must be 23 × 5 = 115. The scores already known add to 32 + 34 + 14 + 22 = 102. The last one is the difference: 115 − 102 = 13. Going from the mean back to the total is the move this question is really testing. Mean times how many gives the total. That one reversal unlocks every missing-value question.
Here are seven numbers: 6, 1, 12, 6, 11, 16, 6. What is the median?
Put them in order first, whichever is being asked for: 1, 6, 6, 6, 11, 12, 16. The median is the middle one. With seven numbers the middle is the fourth, which is 6. Finding the middle of the unsorted list is the mistake to avoid. With an even number of values the median is halfway between the middle two.
The answer is A. Put them in order first, whichever is being asked for: 1, 6, 6, 6, 11, 12, 16. The median is the middle one. With seven numbers the middle is the fourth, which is 6. Finding the middle of the unsorted list is the mistake to avoid. With an even number of values the median is halfway between the middle two.
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