Question

ws 45b - reverse mean v.1 date: 1-28 period:

1. the mean of four numbers is 8. three of the numbers are 2, 4, and 7. find the fourth number.
2. the mean of five numbers is 10. four of the numbers are 2, 8, 11, and 14. find the fifth number.
3. the mean of three numbers is 10. two of the numbers are 4 and 7. find the third number.
4. the mean of four numbers is 9. three of the numbers are 5, 8, and 13. find the fourth number.
5. the mean of four numbers is 9. three of the numbers are 5, 7, and 14. find the fourth number.
6. the mean of three numbers is 11. two of the numbers are 8 and 13. find the third number.
7. the mean of five numbers is 12. four of the numbers are 10, 15, 3, and 6. find the fifth number.
8. the mean of four numbers is 12. three of the numbers are 20, 4, and 15. find the fourth number.
9. the mean of three numbers is 6. two of the numbers are 2 and 12. find the third number.
10. the mean of five numbers is 9. four of the numbers are 7, 13, 15, and 8. find the fifth number.
11. the mean of four numbers is 15. three of the numbers are 12, 16, and 7. find the fourth number.
12. the mean of three numbers is 7. two of the numbers are 3 and 10. find the third number.
13. the mean of four numbers is 11. three of the numbers are 10, 12, and 14. find the fourth number.
14. the mean of five numbers is 10. four of the numbers are 2, 6, 12, and 15. find the fifth number.
15. the mean of three numbers is 9. two of the numbers are 7 and 13. find the third number.

Explanation:

Step1: Recall mean formula

Mean $\bar{x} = \frac{\sum x_i}{n}$, so $\sum x_i = \bar{x} \times n$

Step2: Calculate total sum for each problem

Subtract sum of given numbers from total sum to find missing number.

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Problem 1:

Step1: Calculate total sum

Total sum $= 8 \times 4 = 32$

Step2: Sum given numbers

Sum $= 2 + 4 + 7 = 13$

Step3: Find missing number

Missing number $= 32 - 13 = 19$

Problem 2:

Step1: Calculate total sum

Total sum $= 10 \times 5 = 50$

Step2: Sum given numbers

Sum $= 2 + 8 + 11 + 14 = 35$

Step3: Find missing number

Missing number $= 50 - 35 = 15$

Problem 3:

Step1: Calculate total sum

Total sum $= 10 \times 3 = 30$

Step2: Sum given numbers

Sum $= 4 + 7 = 11$

Step3: Find missing number

Missing number $= 30 - 11 = 19$

Problem 4:

Step1: Calculate total sum

Total sum $= 9 \times 4 = 36$

Step2: Sum given numbers

Sum $= 5 + 8 + 13 = 26$

Step3: Find missing number

Missing number $= 36 - 26 = 10$

Problem 5:

Step1: Calculate total sum

Total sum $= 9 \times 4 = 36$

Step2: Sum given numbers

Sum $= 5 + 7 + 14 = 26$

Step3: Find missing number

Missing number $= 36 - 26 = 10$

Problem 6:

Step1: Calculate total sum

Total sum $= 11 \times 3 = 33$

Step2: Sum given numbers

Sum $= 8 + 13 = 21$

Step3: Find missing number

Missing number $= 33 - 21 = 12$

Problem 7:

Step1: Calculate total sum

Total sum $= 12 \times 5 = 60$

Step2: Sum given numbers

Sum $= 10 + 15 + 3 + 6 = 34$

Step3: Find missing number

Missing number $= 60 - 34 = 26$

Problem 8:

Step1: Calculate total sum

Total sum $= 12 \times 4 = 48$

Step2: Sum given numbers

Sum $= 20 + 4 + 15 = 39$

Step3: Find missing number

Missing number $= 48 - 39 = 9$

Problem 9:

Step1: Calculate total sum

Total sum $= 6 \times 3 = 18$

Step2: Sum given numbers

Sum $= 2 + 12 = 14$

Step3: Find missing number

Missing number $= 18 - 14 = 4$

Problem 10:

Step1: Calculate total sum

Total sum $= 9 \times 5 = 45$

Step2: Sum given numbers

Sum $= 7 + 13 + 15 + 8 = 43$

Step3: Find missing number

Missing number $= 45 - 43 = 2$

Problem 11:

Step1: Calculate total sum

Total sum $= 15 \times 4 = 60$

Step2: Sum given numbers

Sum $= 12 + 16 + 7 = 35$

Step3: Find missing number

Missing number $= 60 - 35 = 25$

Problem 12:

Step1: Calculate total sum

Total sum $= 7 \times 3 = 21$

Step2: Sum given numbers

Sum $= 3 + 10 = 13$

Step3: Find missing number

Missing number $= 21 - 13 = 8$

Problem 13:

Step1: Calculate total sum

Total sum $= 11 \times 4 = 44$

Step2: Sum given numbers

Sum $= 10 + 12 + 14 = 36$

Step3: Find missing number

Missing number $= 44 - 36 = 8$

Problem 14:

Step1: Calculate total sum

Total sum $= 10 \times 5 = 50$

Step2: Sum given numbers

Sum $= 2 + 6 + 12 + 15 = 35$

Step3: Find missing number

Missing number $= 50 - 35 = 15$

Problem 15:

Step1: Calculate total sum

Total sum $= 9 \times 3 = 27$

Step2: Sum given numbers

Sum $= 7 + 13 = 20$

Step3: Find missing number

Missing number $= 27 - 20 = 7$

Answer:

1. 19
2. 15
3. 19
4. 10
5. 10
6. 12
7. 26
8. 9
9. 4
10. 2
11. 25
12. 8
13. 8
14. 15
15. 7