Question

What is the interquartile range (IQR) for the given data set: 13, 14, 17, 18, 23, 27, 28, 31, 34?

1) 14
2) 15.5
3) 21
4) 29.5

Answer 1

The interquartile range (IQR) for the given data set (13, 14, 17, 18, 23, 27, 28, 31, 34) is calculated to be 14, which is the difference between Q3 (29.5) and Q1 (15.5).

Step-by-step explanation:

The interquartile range (IQR) is the measure of the spread of the middle 50 percent of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). For the given data set 13, 14, 17, 18, 23, 27, 28, 31, 34, we need to find Q1 and Q3 to determine the IQR.

• First, arrange the data in ascending order, which is already done.
• Next, find the median (Q2), which for the given data set is 23.
• Q1 is the median of the first half of the data (13, 14, 17, 18), which is the average of 14 and 17, hence Q1 = 15.5.
• Q3 is the median of the second half of the data (27, 28, 31, 34), which is the average of 28 and 31, hence Q3 = 29.5.
• Now calculate IQR: IQR = Q3 - Q1 = 29.5 - 15.5 = 14.

Therefore, the interquartile range (IQR) for the given data set is 14.