Question

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


992 31 716 820 997 986 944 942

Answer 1

To identify the outlier in the data set (992, 31, 716, 820, 997, 986, 944, 942), let's first look at the dataset closely.

The numbers range from 31 (which is significantly lower than the other values) to 997. The majority of the numbers are in the range of 716 to 997, while 31 is an extreme value compared to the rest.

Given this, the outlier in the data set is **31**.

Now, let's consider how removing this outlier would affect the mean of the data set.

1. Calculate the original mean:
- Sum of the data set: \(992 + 31 + 716 + 820 + 997 + 986 + 944 + 942 = 4,428\)
- Number of data points: 8
- Mean = \( \frac{4428}{8} = 553.5\)

2. Remove the outlier (31), and calculate the new mean:
- New sum: \(992 + 716 + 820 + 997 + 986 + 944 + 942 = 4,397\)
- New number of data points: 7
- New Mean = \( \frac{4397}{7} \approx 628.14\)

Since the new mean (approximately 628.14) is greater than the original mean (553.5), we can conclude that removing the outlier (31) would **increase** the mean of the data set.