Question

1. given the following data: 46, 39, 38, 47, 45, 34, 83

a) what effect will the outlier have on the median of the data if the outlier is excluded?
b) what effect will the outlier have on the mean of the data if the outlier is excluded?
c) what effect will the outlier have on the mode of the data if the outlier is excluded?
d) what effect will the outlier have on the range of the data if the outlier is excluded?

Explanation:

Step1: Identify the outlier

The outlier is 83 as it is much larger than the other values.

Step2: Calculate median with all data

Arrange data in ascending order: 34, 38, 39, 45, 46, 47, 83. There are 7 data - points. The median is the 4th value, so median = 45.

Step3: Calculate median without outlier

Remove 83. Data is 34, 38, 39, 45, 46, 47. There are 6 data - points. Median is the average of the 3rd and 4th values, $\frac{39 + 45}{2}=42$. The median decreases.

Step4: Calculate mean with all data

Mean $\bar{x}=\frac{46 + 39+38 + 47+45+34+83}{7}=\frac{332}{7}\approx47.43$.

Step5: Calculate mean without outlier

Mean $\bar{x}=\frac{46 + 39+38 + 47+45+34}{6}=\frac{249}{6}=41.5$. The mean decreases.

Step6: Determine mode with all data

All values occur only once, so there is no mode.

Step7: Determine mode without outlier

All values still occur only once, so there is no mode. The mode is unaffected.

Step8: Calculate range with all data

Range = maximum - minimum = 83 - 34 = 49.

Step9: Calculate range without outlier

Range = 47 - 34 = 13. The range decreases.

Answer:

a) The median decreases.
b) The mean decreases.
c) The mode is unaffected.
d) The range decreases.