Question

select the outlier in the data set. 965 880 883 798 679 995 959 954 106 997 794 968 994 992 998 701 971 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 {965, 880, 883, 798, 679, 995, 959, 954, 106, 997, 794, 968, 994, 992, 998, 701, 971}, most of the values are in the range of 600 - 1000, but 106 is far away from this range. So the outlier is 106.

Step2: Analyze the effect on the mean

The mean of a data set is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. The outlier 106 is a very small value compared to other data - points. When we calculate the mean with this outlier, it pulls the mean down. When we remove it, the sum of the remaining data - points will be divided by a smaller number of elements (n decreases by 1), but the sum will not decrease proportionally as much as the decrease in n. So the mean will increase.

Answer:

1. Outlier: 106
2. Effect on mean: increase