Data and probability · Ages 14–15

Finding an unknown from an average worksheet

Part of: Measures of central tendency

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Data and probability · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The four numbers 24, 13, x and 7 have a mean of 14. x =
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2.The four numbers 9, 20, x and 10 have a mean of 23. x =
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3.9 data have a mean of 34. One is taken out, and the mean of the other 8 is 34 − 2. What was taken out?
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4.The five numbers 34, x, 16, 12 and 19 have a mean of 23. Their sum is , so x = .
Fill in each blank
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5.6 data have a mean of 14. One more is put in, and the mean of the 7 becomes 14 + 2. What was put in?
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6.7 data have a mean of 39. One is taken out, and the mean of the other 6 is 39 − 1. What was taken out?
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7.The five numbers 31, x, 12, 27 and 24 have a mean of 19. Their sum is , so x = .
Fill in each blank
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8.Five data in order, smallest first, are 33, 39, x, 48 and y; their median is 45 and their mean 44. y =
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9.Six data in order, smallest first, are 27, 29, 34, x, 45, 51, and their median is 36. x =
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10.Six data in order, smallest first, are 16, 23, 25, x, 41, 42, and their median is 29. x =
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11.Four numbers have a mean of 10; three of them are 17, 7 and 15, and the fourth is 1.
True or false?
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12.Four numbers have a mean of 14; three of them are 14, 21 and 12, and the fourth is 9.
True or false?
Answer:

13.Chi-keung averaged 14 points over the first five basketball games. After the sixth, the six games average 16. The first five make points, all six , so the sixth game was points.
Fill in each blank
Working:
Answer:
14.Ming plays a shooting game and scores 81, 88, 73 and 78 in the first four rounds. For a mean of 82 over five rounds, at least how many points does the fifth round need?
Working:
Answer:
15.A dance troupe's 30 members have a mean weight of 64 kg. 5 members, with a mean weight of 76 kg, leave. What is the mean weight of the other 25, in kg?
Working:
Answer:
16.Six basketball players' heights (cm), shortest first, are 144, 146, 149, h, 156, 160, and the median height is 151 cm. The middle two add up to cm, so h = .
Fill in each blank
Working:
Answer:
17.Ka-lok averaged 16 points over the first five basketball games. After the sixth, the six games average 17. The first five make points, all six , so the sixth game was points.
Fill in each blank
Working:
Answer:
18.Six basketball players' heights (cm), shortest first, are 151, 153, 155, h, 163, 165, and the median height is 157 cm. The middle two add up to cm, so h = .
Fill in each blank
Working:
Answer:

Show the answers and working

Finding an unknown from an average worksheet: Answers and working

1. 12
The sum = 14 × 4 = 56, so x = 56 − 24 − 13 − 7 = 12.
2. 53
The sum = 23 × 4 = 92, so x = 92 − 9 − 20 − 10 = 53.
3. 50
The old sum is 306 and the rest add up to 8 × (34 − 2) = 256, so 306 − 256 = 50 came out.
4. 115, 34
Sum = mean × how many = 23 × 5 = 115; x = 115 − 34 − 16 − 12 − 19 = 34.
5. 28
The old sum is 6 × 14 = 84; the new 7 × (14 + 2) = 112; so 112 − 84 = 28 went in.
6. 45
The old sum is 273 and the rest add up to 6 × (39 − 1) = 228, so 273 − 228 = 45 came out.
7. 95, 1
Sum = mean × how many = 19 × 5 = 95; x = 95 − 31 − 12 − 27 − 24 = 1.
8. 55
The median of five is the 3rd, so x = 45; the sum = 44 × 5 = 220, so y = 220 − 33 − 39 − 45 − 48 = 55.
9. 38
The median of six is the mean of the 3rd and 4th: (34 + x) ÷ 2 = 36, so x = 2 × 36 − 34 = 38.
10. 33
The median of six is the mean of the 3rd and 4th: (25 + x) ÷ 2 = 29, so x = 2 × 29 − 25 = 33.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 70, 96, 26
5 × 14 = 70, 6 × 16 = 96, so the sixth game 96 − 70 = 26.
14. 90 points
Five rounds need at least 82 × 5 = 410, so the fifth at least 410 − 81 − 88 − 73 − 78 = 90.
15. 61.6 kg
The whole troupe 30 × 64 = 1920 kg, those leaving 5 × 76 = 380 kg: (1920 − 380) ÷ 25 = 61.6 kg.
16. 302, 153
The median is the mean of the 3rd and 4th: 149 + h = 2 × 151 = 302, so h = 302 − 149 = 153.
17. 80, 102, 22
5 × 16 = 80, 6 × 17 = 102, so the sixth game 102 − 80 = 22.
18. 314, 159
The median is the mean of the 3rd and 4th: 155 + h = 2 × 157 = 314, so h = 314 − 155 = 159.

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