Question

Select the outlier in the data set.
If the outlier were removed from the data set, would the mean increase or decrease?
38 503 576 678 738 757 766 789 831 837 904 910 911 943 954

Answer 1

To identify the outlier in the given data set, we can use the interquartile range (IQR) method or look for a value that is distinctly different from the others.

The data set is:
38, 503, 576, 678, 738, 757, 766, 789, 831, 837, 904, 910, 911, 943, 954

The number 38 appears significantly lower than the rest of the values, which range from 503 to 954. Thus, 38 is the outlier.

Next, to determine whether the mean would increase or decrease if the outlier (38) were removed, we can calculate the mean before and after its removal.

**Step 1: Calculate the mean before removing the outlier.**
- Sum of the data set = 38 + 503 + 576 + 678 + 738 + 757 + 766 + 789 + 831 + 837 + 904 + 910 + 911 + 943 + 954 = 10372
- Number of values = 15
- Mean = Sum / Count = 10372 / 15 ≈ 691.47

**Step 2: Calculate the mean after removing the outlier (38).**
- New sum = 503 + 576 + 678 + 738 + 757 + 766 + 789 + 831 + 837 + 904 + 910 + 911 + 943 + 954 = 10334
- New number of values = 14
- New mean = New Sum / New Count = 10334 / 14 ≈ 737.43

Now we can compare the means:
- Mean with outlier = 691.47
- Mean without outlier = 737.43

Since the mean after removing the outlier (737.43) is greater than the mean before removing it (691.47), we conclude that:

1. The outlier is **38**.
2. The mean would **increase** if the outlier were removed.