Question

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


90 68 52 417 92 83 42 60 87

Answer 1

To identify the outlier in the data set \(90, 68, 52, 417, 92, 83, 42, 60, 87\), we can look for a number that is significantly different from the others.

The majority of the numbers range from 42 to 92, while 417 is much larger than the rest of the numbers. Therefore, 417 is the outlier.

Next, we analyze the effect of removing the outlier on the mean.

1. **Calculate the mean of the original data set:**
\[
\text{Mean} = \frac{\text{Sum of the numbers}}{\text{Total number of entries}} = \frac{90 + 68 + 52 + 417 + 92 + 83 + 42 + 60 + 87}{9}
\]
\[
= \frac{919}{9} \approx 102.11
\]

2. **Calculate the mean without the outlier (417):**
\[
\text{New Sum} = 90 + 68 + 52 + 92 + 83 + 42 + 60 + 87 = 522
\]
\[
\text{New Mean} = \frac{522}{8} = 65.25
\]

When we remove the outlier (417), the mean decreases from approximately 102.11 to 65.25.

**Conclusion:**
- The outlier is **417**.
- The mean would **decrease** if the outlier were removed from the data set.