Question

select the outlier in the data set. 84 90 92 93 95 96 98 605 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 {84, 90, 92, 93, 95, 96, 98, 605}, 605 is much larger than the other values.

Step2: Analyze the effect on the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. The outlier 605 is a very large value. When calculating the mean with 605 included, it pulls the mean upwards. When it is removed, the sum of the remaining data points is smaller and the number of data points $n$ is also smaller, but the reduction in the sum is proportionally larger than the reduction in $n$. So the mean will decrease.

Answer:

605
decrease