Question

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


2398 562 537 652 791 876 946 744

Answer 1

To identify the outlier in the data set \(2398, 562, 537, 652, 791, 876, 946, 744\), we should first view the data points relative to each other.

1. **Identify the Outlier:**
- The values are:
- 2398
- 562
- 537
- 652
- 791
- 876
- 946
- 744

Here, it is clear that **2398** is significantly larger than the other values, which are clustered within a lower range (between 537 and 946). Therefore, **2398** is the outlier.

2. **Calculating the Mean:**
Let's calculate the mean with and without the outlier:

- **Original Mean:**
\[
\text{Mean} = \frac{2398 + 562 + 537 + 652 + 791 + 876 + 946 + 744}{8}
\]
\[
= \frac{6290}{8} = 786.25
\]

- **Mean without the Outlier (2398):**
\[
\text{Mean} = \frac{562 + 537 + 652 + 791 + 876 + 946 + 744}{7}
\]
\[
= \frac{4208}{7} \approx 601.14
\]

3. **Conclusion:**
When the outlier (2398) is removed from the data set, the mean decreases from approximately 786.25 to approximately 601.14.

Thus, the outlier is **2398**, and removing it would cause the mean to **decrease**.