Question

finding missing data point using mean
we can determine the missing number in a series if we know the mean by using the following formula:
mean = \frac{sum of given numbers + (unknown number)}{total numbers}
example: 25, 27, ?, 30 mean = 26
steps

1. multiply the number of total numbers you have by the mean (26 x 4 = 104)
2. add the 3 numbers you know (25 + 27 + 30 = 82)
3. find the difference (subtract) between 104 and 82 (104 - 82 = 22) - answer = 22

questions fill in the table below to find the missing data point
ex) 9, 16, ?, 22, 12, 19 mean 15 calculations 1) 15 x 6 = 90 2) 9 + 16 + 22 + 12 + 19 = 78 3) 90 - 78 = 12 missing data point 12

1. 8, ?, 7, 13, 12, 11 mean 11 calculations missing data point 15
2. 27, 19, 14, ?, 53 mean 29 calculations missing data point 32
3. 37, 22, 48, ?, 62, 77 mean 50 calculations missing data point 54
4. -8, -5, -13, ? mean -8 calculations missing data point
5. -15, ?, 17, -17, -7 mean -2 calculations missing data point

Explanation:

Step1: Multiply the number of total numbers by the mean

For question 4: There are 4 numbers, mean is -8. So \( -8\times4=-32 \)
For question 5: There are 5 numbers, mean is -2. So \( -2\times5 = -10 \)

Step2: Add the known numbers

For question 4: The known numbers are -8, -5, -13. Their sum is \( -8+( - 5)+(-13)=-26 \)
For question 5: The known numbers are -15,17, - 17, -7. Their sum is \( -15 + 17+( - 17)+(-7)=-22 \)

Step3: Find the difference (subtract)

For question 4: Let the missing number be \(x\). We know that \(-32=-26 + x\), so \(x=-32-( - 26)=-6\)
For question 5: Let the missing number be \(y\). We know that \(-10=-22 + y\), so \(y=-10-( - 22)=12\)

Answer:

1. -6
2. 12