Mean practice questions

Mean questions

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1. 1MeanFoundation

   What is the mean of 4, 6, 7, 9, and 14?What is the mean of 4, 6, 7, 9, and 14?

   • A88
   • B1010
   • C77
   • D99
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   Answer: 88

   Add the values and divide by how many there are: 405 = 8. The mean needs both numbers, and the count is the half that gets forgotten when the list is long.Add the values and divide by how many there are: 40/5 = 8. The mean needs both numbers, and the count is the half that gets forgotten when the list is long.

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2. 2MeanFoundation

   Five numbers have a mean of 12. Enter their sum.Five numbers have a mean of 12. Enter their sum.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 6060

   The mean is the sum divided by the count, so the sum is 12 × 5 = 60.The mean is the sum divided by the count, so the sum is 12 × 5 = 60.

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3. 3MeanStandard

   A student's four test scores average 78. What score on a fifth test would raise the average to 80?A student's four test scores average 78. What score on a fifth test would raise the average to 80?

   • A8686
   • B9090
   • C8888
   • D8282
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   Answer: 8888

   Four scores at 78 total 312. Five scores at 80 total 400. The fifth score must be 400 - 312 = 88.Four scores at 78 total 312. Five scores at 80 total 400. The fifth score must be 400 - 312 = 88.

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4. 4MeanStandard

   The mean of five numbers is 20. Two of them are 14 and 26. What is the mean of the other three?The mean of five numbers is 20. Two of them are 14 and 26. What is the mean of the other three?

   • A1818
   • B2020
   • C2424
   • D2222
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   Answer: 2020

   The five total 100, and 14 + 26 = 40, so the other three total 60 and average 20. The two removed happen to average 20 themselves, which is why the rest are unaffected.The five total 100, and 14 + 26 = 40, so the other three total 60 and average 20. The two removed happen to average 20 themselves, which is why the rest are unaffected.

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5. 5MeanStandard

   Rainfall at a weather station over five months was 42 mm, 55 mm, 38 mm, 61 mm and 44 mm. What is the mean monthly rainfall?Rainfall at a weather station over five months was 42 mm, 55 mm, 38 mm, 61 mm and 44 mm. What is the mean monthly rainfall?

   • A44 mm44 mm
   • B48 mm48 mm
   • C55 mm55 mm
   • D46 mm46 mm
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   Answer: 48 mm48 mm

   The five values total 240 mm, and 2405 = 48 mm. The choice 44 is the middle value when the list is sorted, which is the median, and 55 is one reading rather than a summary of all five.The five values total 240 mm, and 240/5 = 48 mm. The choice 44 is the middle value when the list is sorted, which is the median, and 55 is one reading rather than a summary of all five.

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6. 6MeanStandard

   Six readings were 12, 15, 11, 18, 14 and 20. What is their mean?Six readings were 12, 15, 11, 18, 14 and 20. What is their mean?

   • A1414
   • B1515
   • C1616
   • D14.514.5
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   Answer: 1515

   The six values total 90, and 906 = 15. The choice 14.5 is the median — the average of the third and fourth values once sorted — which happens to differ here.The six values total 90, and 90/6 = 15. The choice 14.5 is the median — the average of the third and fourth values once sorted — which happens to differ here.

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7. 7MeanStandard

   Five numbers have a mean of 18. Four of them are 12, 20, 15 and 22. Enter the fifth number.Five numbers have a mean of 18. Four of them are 12, 20, 15 and 22. Enter the fifth number.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 2121

   The five must total 5 × 18 = 90. The four given add to 69, so the fifth is 90 - 69 = 21. Working from the total rather than from the mean is what makes this straightforward.The five must total 5 × 18 = 90. The four given add to 69, so the fifth is 90 - 69 = 21. Working from the total rather than from the mean is what makes this straightforward.

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8. 8MeanStandard

   Six numbers have a mean of 14. Five of them are 9, 17, 12, 20 and 11. Enter the sixth.Six numbers have a mean of 14. Five of them are 9, 17, 12, 20 and 11. Enter the sixth.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 1515

   The six must total 6 × 14 = 84. The five given add to 69, so the sixth is 84 - 69 = 15.The six must total 6 × 14 = 84. The five given add to 69, so the sixth is 84 - 69 = 15.

   How did you do?Got itMissed it
9. 9MeanStandard

   Seven numbers have a mean of 22. Six of them are 19, 25, 18, 27, 21 and 20. Enter the seventh.Seven numbers have a mean of 22. Six of them are 19, 25, 18, 27, 21 and 20. Enter the seventh.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 2424

   The seven must total 7 × 22 = 154. The six given add to 130, so the seventh is 154 - 130 = 24.The seven must total 7 × 22 = 154. The six given add to 130, so the seventh is 154 - 130 = 24.

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10. 10MeanChallenge

    The list 4, 8, 9, 11, 13 gains a sixth number, which raises the mean of the list to 10. Enter the sixth number.The list 4, 8, 9, 11, 13 gains a sixth number, which raises the mean of the list to 10. Enter the sixth number.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 1515

    The five numbers sum to 45. Six numbers with a mean of 10 sum to 60, so the new number is 60 - 45 = 15.The five numbers sum to 45. Six numbers with a mean of 10 sum to 60, so the new number is 60 - 45 = 15.

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11. 11MeanChallenge

    Six numbers have a mean of 14. If the largest number is removed, the mean of the remaining five is 12. What was the largest number?Six numbers have a mean of 14. If the largest number is removed, the mean of the remaining five is 12. What was the largest number?

    • A2424
    • B1818
    • C2626
    • D2020
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    Answer: 2424

    Six numbers at a mean of 14 sum to 84; five at a mean of 12 sum to 60. The removed value is the difference, 84 - 60 = 24.Six numbers at a mean of 14 sum to 84; five at a mean of 12 sum to 60. The removed value is the difference, 84 - 60 = 24.

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