Question

( 71 + 91 + 82 + 90 + 88 + 61 + 70 = 553 What is the missing data set that would make the mean equal 80?

Answer 1

To find the missing data set that will make the mean equal to 80 when combined with the existing scores, we can follow these steps:

1. **Determine the total number of data points**:
We currently have 7 scores (71, 91, 82, 90, 88, 61, and 70) and we want to add 1 more score (let's call it x). So the total number of data points will be 8.

2. **Calculate the desired total score for the mean**:
The mean is calculated as:

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

If we want the mean to be 80 with 8 data points, then we can set up the equation:

\[
80 = \frac{\text{Total Sum}}{8}
\]

Therefore, the total sum should be:

\[
\text{Total Sum} = 80 \times 8 = 640
\]

3. **Calculate the sum of the existing scores**:
We already know that the sum of the existing scores is 553.

4. **Determine the missing score**:
Now we will set up the equation to find x:

\[
553 + x = 640
\]

Solving for x:

\[
x = 640 - 553
\]
\[
x = 87
\]

Therefore, the missing score that would make the mean equal to 80 is **87**.