Final answer:
The outlier, 256, increased the range of the data set by 171, which is calculated by finding the difference between the range including the outlier (218) and the range excluding it (47).
Step-by-step explanation:
The calculation required to find out by how much the outlier in the data set increases the range is straightforward. First, we need to identify the potential outlier in the data set, which is the value that is distinctly larger than the rest: 256. Next, we find the range of the data set including the outlier by subtracting the smallest value from the largest value, which is 256 - 38 = 218. Then we find the range without the outlier by identifying the next largest value which is 85, and calculate the range again: 85 - 38 = 47. Lastly, we subtract the range without the outlier from the range with the outlier to find the increase in range due to the outlier: 218 - 47 = 171.
Thus, the outlier increased the range of the data set by 171.