Question

select the outlier in the data set. 44 46 51 58 60 63 64 65 68 69 73 76 77 79 81 86 99 415 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 given data set, most of the values are in the range of 44 - 99, while 415 is much larger. So 415 is the outlier.

Step2: Analyze the effect on the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. The outlier 415 is a very large value. When we calculate the mean with 415 included, it pulls the mean upwards. When we remove 415, the sum of the remaining values will be smaller and the number of data - points $n$ will also be smaller, but the proportionate decrease in the sum is larger than the decrease in $n$. So the mean will decrease.

Answer:

415
decrease