Final answer:
The interquartile range (IQR) for the data set is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), resulting in an IQR of 24.
Step-by-step explanation:
Calculating the Interquartile Range (IQR)
The interquartile range (IQR) measures the spread of the middle 50 percent of a data set and is the difference between the third quartile (Q3) and the first quartile (Q1). To find the first and third quartiles for the given data set, we would list the data in ascending order, which is already done, and then divide the set into four equal parts. The middle value between the smallest number and the median of the dataset is Q1, and the middle value between the median and the largest number in the dataset is Q3.
IQR = Q3 - Q1. In this case, we have ten data points: 12, 17, 22, 26, 33, 37, 44, 46, 53, 59. The median (or Q2) is the average of the 5th and 6th values, which are 33 and 37, so the median is (33 + 37) / 2 = 35. The first quartile (Q1) is the median of the first half of the data, which are 12, 17, 22, 26, and 33. So Q1 is 22. The third quartile (Q3) is the median of the second half of the data, which are 37, 44, 46, 53, 59. So Q3 is 46.
The interquartile range is therefore 46 - 22 = 24.
As for the range of the entire set, it is simply the largest value minus the smallest value, which is 59 - 12 = 47.