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 \( x \) in the data set that would make the mean equal to 80, we first need to calculate the current sum of the known values and then use the formula for the mean.

1. **Calculate the current sum of the known values**:
\[
71 + 91 + 82 + 90 + 88 + 61 + 70 = 453
\]

2. **Determine the total number of values**:
In total, we have 7 known values and 1 unknown value \( x \), which gives us a total of 8 values.

3. **Set up the equation for the mean**:
The mean of the data set is given by the formula:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}
\]
In this case, we want the mean to be 80:
\[
80 = \frac{453 + x}{8}
\]

4. **Solve for \( x \)**:
First, multiply both sides of the equation by 8:
\[
80 \times 8 = 453 + x
\]
\[
640 = 453 + x
\]

Next, isolate \( x \) by subtracting 453 from both sides:
\[
x = 640 - 453
\]
\[
x = 187
\]

5. **Conclusion**:
The missing value in the data set that would make the mean equal 80 is \( \boxed{187} \).