What is the interquartile range (IQR) of the following data set?
7, 4, 3, 5, 2, 6, 3
First, let's arrange the data set in ascending order:
2, 3, 3, 4, 5, 6, 7
The first quartile (Q1) is the median of the lower half of the data set. Since there are 7 numbers in the data set, the lower half consists of the first 3 numbers. Thus, Q1 is the median of the numbers 2, 3, and 3, which is 3.
The third quartile (Q3) is the median of the upper half of the data set. Since there are 7 numbers in the data set, the upper half consists of the last 3 numbers. Thus, Q3 is the median of the numbers 5, 6, and 7, which is 6.
The interquartile range (IQR) is defined as the difference between the third quartile (Q3) and the first quartile (Q1). In this case, IQR = Q3 - Q1 = 6 - 3 = 3.
Therefore, the interquartile range (IQR) of the given data set is 3.