Question

Select the outlier in the data set.
If the outlier were removed from the data set, would the mean increase or decrease?


95 16 89 98 63 85 99 83 75 86 90 79 93

Answer 1

To identify the outlier in the given data set, we can analyze the values for any that are significantly higher or lower than the others.

The provided data set is:
- 95, 16, 89, 98, 63, 85, 99, 83, 75, 86, 90, 79, 93

Looking at these values, 16 stands out as an outlier because it is much lower than the rest of the numbers, which are clustered around the 80s and 90s.

Now, if we remove the outlier (16), we need to consider how this affects the mean of the data set.

1. First, calculate the mean of the original data set:
\[
\text{Mean} = \frac{(95 + 16 + 89 + 98 + 63 + 85 + 99 + 83 + 75 + 86 + 90 + 79 + 93)}{13}
\]
\[
= \frac{1074}{13} \approx 82.62
\]

2. Now, calculate the mean after removing the outlier (16):
\[
\text{New Mean} = \frac{(95 + 89 + 98 + 63 + 85 + 99 + 83 + 75 + 86 + 90 + 79 + 93)}{12}
\]
\[
= \frac{1056}{12} \approx 88.00
\]

After removing the outlier, the mean increases from approximately 82.62 to approximately 88.00.

### Conclusion:
- The outlier is **16**.
- Removing the outlier would cause the mean to **increase**.