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 ,__

Answer 1

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

1. **Identify the data set**: The given data set is:
\[
71, 91, 82, 90, 88, 61, 70, x
\]
where \( x \) is the missing value.

2. **Determine the number of values**: There are 7 known values, plus the missing value \( x \). Therefore, there are a total of \( 8 \) values in the data set.

3. **Set up the equation for the mean**: The mean is calculated as the sum of all values divided by the number of values. We want the mean to be 80:
\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = 80
\]
So, we can write the equation:
\[
\frac{(71 + 91 + 82 + 90 + 88 + 61 + 70 + x)}{8} = 80
\]

4. **Calculate the sum of the known values**:
\[
71 + 91 + 82 + 90 + 88 + 61 + 70 = 71 + 91 = 162
\]
\[
162 + 82 = 244
\]
\[
244 + 90 = 334
\]
\[
334 + 88 = 422
\]
\[
422 + 61 = 483
\]
\[
483 + 70 = 553
\]
Thus, the sum of the known values is \( 553 \).

5. **Substituting and solving for \( x \)**:
Now we substitute this sum back into our mean equation:
\[
\frac{553 + x}{8} = 80
\]
To eliminate the fraction, multiply both sides by 8:
\[
553 + x = 640
\]
Now, we solve for \( x \) by subtracting 553 from both sides:
\[
x = 640 - 553 = 87
\]

6. **Conclusion**: The missing value \( x \) that would make the mean equal to 80 is:
\[
\boxed{87}
\]