Question

select the outlier in the data set.
89 79 97 94 61 85 73 10 78 83
95 46 80 91
if the outlier were removed from the data set, would the mean increase or decrease?
increase decrease

Explanation:

Step1: Identify the outlier

An outlier is a value that is significantly different from the other values in the data set. Looking at the data: 89, 79, 97, 94, 61, 85, 73, 10, 78, 83, 95, 46, 80, 91. Most values are in the range of 46 - 97, but 10 is much lower than the rest. So the outlier is 10.

Step2: Analyze the effect on the mean

The mean is the sum of all values divided by the number of values. The outlier (10) is a very small number, so it pulls the mean down. If we remove this small outlier, the sum of the remaining values will be larger (since we're removing a small number), and the number of values will decrease by 1. Let's check with a simple example: suppose we have values [10, 50, 60]. The mean is (10 + 50 + 60)/3 = 40. Remove 10: (50 + 60)/2 = 55, which is an increase. So removing a low outlier increases the mean.

Answer:

The outlier is 10. If the outlier is removed, the mean will increase.