Question

What is the interquartile range of this data set? 1, 4, 10, 11, 29, 40, 42, 61, 65, 84, 91.

A. 55
B. 65
C. 40
D. 10

Answer 1

The interquartile range (IQR) for the dataset is 72, which is the difference between the third quartile (74.5) and the first quartile (2.5). None of the provided options match this value, suggesting a possible error in the question or options.

Step-by-step explanation:

The interquartile range (IQR) of a dataset is the difference between the third quartile (Q3) and the first quartile (Q1), which represents the spread of the middle 50 percent of the data. To find the interquartile range for the given data set (1, 4, 10, 11, 29, 40, 42, 61, 65, 84, 91), we first need to arrange the data in ascending order, which is already done, then find the first and third quartiles.

• The median (second quartile) of the dataset is 29, as it is the middle value.
• The first quartile (Q1) will be the median of the lower half of the data: (1 + 4) / 2 = 2.5.
• The third quartile (Q3) will be the median of the upper half of the data: (65 + 84) / 2 = 74.5.
• The IQR is then Q3 - Q1, which is 74.5 - 2.5 = 72.

Hence, the interquartile range is not one of the provided options (A. 55, B. 65, C. 40, D. 10). It seems there might be a mistake in the question or the provided options.