Find a missing value given the mean

The mean represents the equal-share value of a data set: for $n$ values, the total is $n$ times the mean, even though the mean need not be one of the data values. Given the mean and all but one value, the missing value is found by subtracting the known values from the total and checking the result in context; this applies to unweighted data sets with whole-number or terminating-decimal values, not weighted means or advanced statistical inference.

Detailed Explanation: Find a missing value given the mean

The mean is the equal-share value of a data set. To find a missing value:

Count the total number of values.
Multiply the mean by the number of values to find the total.
Add the known values.
Subtract the known total from the overall total.

Example

The mean of five numbers is $8$ . Four of the numbers are $(6, 9, 7,)$ and $(10)$ . What is the missing number?

Step 1: Find the total of all five numbers.

5 \times 8 = 40

So, all five numbers together must total $(40)$ .

Step 2: Add the known numbers.

6+9+7+10=32

Step 3: Subtract to find the missing number.

40-32=8

The missing number is $\boxed{8}$ .

Check: The numbers are $(6, 9, 7, 10,)$ and $8$ . Their total is $(40)$ , and

40 \div 5=8

so the mean is correct.

Learn by doing: Find a missing value given the mean

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Statistics - Mean with Value Missing

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