What is the interquartile range for this set of data? 50, 78, 64, 39, 97, 88, 43, 47, 73, 41, 56, 84, 67, 72, 92, 59
A) 16
B) 24
C) 28
D) 58

Question

Quizplus · Accepted Answer

To find the interquartile range, we first need to find the median (Q2) of the data set. The median is the middle number when the data set is ordered from least to greatest. In this case, since there are 16 numbers, the median is the average of the 8th and 9th numbers, which are 73 and 41. So Q2 = (73+41)/2 = 57.

Next, we need to find the median of the lower half of the data set, which is called the first quartile (Q1). To do this, we put the lower half of the numbers (1st to 8th) in order and find the median. Q1 is the middle number of the lower half. In this case, Q1 is the average of the 4th and 5th numbers, which are 56 and 47. So Q1 = (56+47)/2 = 51.5.

Finally, we find the median of the upper half of the data set, which is called the third quartile (Q3). We put the upper half of the numbers (9th to 16th) in order and find the median. Q3 is the middle number of the upper half. In this case, Q3 is the average of the 13th and 14th numbers, which are 84 and 67. So Q3 = (84+67)/2 = 75.5.

The interquartile range is the difference between the third and first quartiles, so IQR = Q3 - Q1 = 75.5 - 51.5 = 24. Therefore, the best choice is C) 28.

What Is the Interquartile Range for This Set of Data