Exercise 6 Page 742

We are asked how an outlier affects the range of a set of data. Recall that an outlier is a data value that is much greater than or much less than the other values in the data set. Let's take a look at an example data set that has an outlier. cccc 1 & 5 & 2 & 1 2 & 99 & 4 & 3The value 99 is much greater than the other data values. Therefore, we can call this data value an outlier. Now we will find the range of the data set and the range of the same set but without the outlier. To calculate the range, we first need to find the greatest and the least data values in the data sets. Data Set cccc 1 & 5 & 2 & 1 2 & 99 & 4 & 3 [1em] Data Set Without the Outlier cccc 1 & 5 & 2 & 1 2 & 99 & 4 & 3 For each data set, the least data value is 1. The greatest data value in the first set, which happens to be the outlier, is 99. The greatest value of the set without the outlier is 5. To find the ranges, we need to calculate the differences between the greatest and the least values.

Notice that the range is significantly less than 98 when the outlier is removed. Therefore, the outlier increased the range of the data set. Since outliers are always much greater than or much less than the other data values, the spread of the data is increased and the range of the data is greater.