Final answer:
The interquartile range (IQR) for the dataset {11, 7, 31, 3, 2, 37, 41, 23} is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), which is 29.
Step-by-step explanation:
The interquartile range (IQR) is a measure of statistical dispersion and is the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. To find the IQR for the given dataset {11, 7, 31, 3, 2, 37, 41, 23}, we first need to order the data from smallest to largest: {2, 3, 7, 11, 23, 31, 37, 41}. The first quartile (Q1) is the median of the lower half, which includes {2, 3, 7, 11}, and hence Q1 is 5 (average of 3 and 7). The third quartile (Q3) is the median of the upper half, which includes {23, 31, 37, 41}, and Q3 is 34 (average of 31 and 37). Therefore, the IQR is Q3 - Q1 which is 34 - 5 = 29.