In the data set below, what is the interquartile range?
2036363638445255
To find the interquartile range (IQR), we first need to determine the values of the first quartile (Q1) and the third quartile (Q3).
1. Arrange the numbers in ascending order:
20, 36, 36, 38, 44, 52, 55
2. Find the median (Q2) of the data set:
Q2 = (38 + 44) / 2 = 41
3. Find Q1 and Q3:
Q1 = median of the lower half of the data set: (20, 36, 36) = 36
Q3 = median of the upper half of the data set: (44, 52, 55) = 52
4. Calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 52 - 36
IQR = 16
Therefore, the interquartile range of the data set is 16.