Question

What is the missing value in the data set that would make the mean equal 80?
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 start with the formula for the mean:

\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}
\]

Let \( x \) be the missing value. The data set has 8 values, including the missing value. The sum of the known values is:

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

Including the missing value \( x \), the sum is \( 453 + x \). Since the mean needs to be 80, we set up the equation:

\[
\frac{453 + x}{8} = 80
\]

Multiplying both sides by 8 to eliminate the fraction:

\[
453 + x = 640
\]

Now, solve for \( x \):

\[
x = 640 - 453
\]
\[
x = 187
\]

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