The six measurements that follow are furnace temperatures recorded on successive batches in a semiconductor manufacturing process (units are degrees Fahrenheit): 953, 950, 948, 955, 951, 955. (a) Calculate the sample mean, sample variance, and sample standard deviation. (b) Find the range and median. How much could the largest temperature measurement increase without changing the median value? (c) Find Q1, Q3, and the IQR.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.