Question

select the outlier in the data set. 96 63 99 80 83 95 85 93 87 28 82 76 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 data - point that is significantly different from other data - points. In the set {96, 63, 99, 80, 83, 95, 85, 93, 87, 28, 82, 76}, most of the values are in the range of 60 - 100. The value 28 is much lower than the rest, so 28 is the outlier.

Step2: Analyze the effect on the mean

The mean of a data - set is calculated as $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. The outlier 28 is a very low value. When we calculate the mean with this value included, it pulls the mean down. When we remove it, the sum of the remaining values will be divided by a smaller number of elements, but since the removed value was a very low one, the new mean will be higher. So the mean will increase.

Answer:

The outlier is 28.
increase