Question

What is the missing value in the data set that would make the mean equal 80? Show your work or explain how you got your answer.

{71, 91, 82, 90, 88, 61, 70, __ }

(4 points)

Answer 1

To find the missing value that would make the mean of the data set equal to 80, we can follow these steps:

1. **Determine the number of data points**: In the dataset provided, there are 7 known numbers and one missing number. This means there will be a total of 8 data points once the missing number is included.

2. **Calculate the desired total sum of all data points**: The mean is calculated by dividing the total sum of all data points by the number of data points. We want the mean to equal 80, and since there will be 8 data points, we can set up the equation:

\[
\text{Mean} = \frac{\text{Total Sum}}{\text{Number of Data Points}}
\]

To find the total sum when the mean is 80, we can rearrange this:

\[
\text{Total Sum} = \text{Mean} \times \text{Number of Data Points} = 80 \times 8 = 640
\]

3. **Calculate the sum of the known data points**: Now we need to sum the known values of the dataset:

\[
71 + 91 + 82 + 90 + 88 + 61 + 70 = 453
\]

4. **Set up an equation to find the missing value**: Let \( x \) be the missing value. The equation can be formed as follows:

\[
453 + x = 640
\]

5. **Solve for \( x \)**:

\[
x = 640 - 453 = 187
\]

So, the missing value that would make the mean equal 80 is **187**.

**Final Answer: 187**