To calculate the lower quartile (Q1):
1. Arrange the data in order from smallest to largest: 20,22,25,28,29,30,32,33,34
2. Calculate the median (middle value) of the lower half of the data set. In this case, the lower half is: 20, 22, 25, 28. Therefore, the median is (22+25)/2 = 23.5.
This value is the lower quartile (Q1).
To calculate the upper quartile (Q3):
1. Arrange the data in order from smallest to largest: 20,22,25,28,29,30,32,33,34
2. Calculate the median (middle value) of the upper half of the data set. In this case, the upper half is: 30, 32, 33, 34. Therefore, the median is (32+33)/2 = 32.5.
This value is the upper quartile (Q3).
To calculate the interquartile range (IQR):
1. IQR = Q3 - Q1
2. In this case, IQR = 32.5 - 23.5 = 9.