Question

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


508 687 306 379 387 995 277 596 471 554 242 386 720 972 539 7461 228 663

Answer 1

To identify the outlier in the data set, we can look for values that are significantly higher or lower than the others. The provided data set is:

508, 687, 306, 379, 387, 995, 277, 596, 471, 554, 242, 386, 720, 972, 539, 7461, 228, 663

Analyzing the data, it is clear that 7461 is significantly higher than the rest of the values, which range only from 228 to 995. Thus, 7461 is the outlier.

Now, if we remove the outlier (7461) from the data set, we can determine how it affects the mean.

To compute the mean, we first sum the remaining values and then divide by the number of values.

### Calculating the Mean Before Removal:

Original data set (with outlier):
- 18 values in total.

Sum of all values:
508 + 687 + 306 + 379 + 387 + 995 + 277 + 596 + 471 + 554 + 242 + 386 + 720 + 972 + 539 + 7461 + 228 + 663 = 8302

Mean gives:
\[
\text{Mean} = \frac{8302}{18} \approx 461.22
\]

### Calculating the Mean After Removal:

Data set without outlier:
- 17 values in total.

Sum of values after removing 7461:
508 + 687 + 306 + 379 + 387 + 995 + 277 + 596 + 471 + 554 + 242 + 386 + 720 + 972 + 539 + 228 + 663 = 5197

Mean gives:
\[
\text{Mean} = \frac{5197}{17} \approx 305.71
\]

### Conclusion:

- **Outlier**: 7461
- **Mean with outlier**: approximately 461.22
- **Mean without outlier**: approximately 305.71

After removing the outlier, the mean decreases.