Calculate the interquartile range of the following data.
35,20,41,48,79,83,83,97,120
Q1=
Q3=
IQR=
Valus lower then and higher than are considered outliners.
To calculate the interquartile range (IQR), we first need to find the first quartile (Q1) and third quartile (Q3).
Step 1: Arrange the data in numerical order:
20, 35, 41, 48, 79, 83, 83, 97, 120
Step 2: Calculate the median of the data set, which is the middle value:
Median = (48 + 79) / 2 = 63.5
Step 3: Split the data set into two halves based on the median:
Lower half: 20, 35, 41
Upper half: 83, 83, 97, 120
Step 4: Calculate Q1, which is the median of the lower half:
Q1 = (35 + 41) / 2 = 38
Step 5: Calculate Q3, which is the median of the upper half:
Q3 = (83 + 97) / 2 = 90
Step 6: Calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 90 - 38 = 52
Therefore, the interquartile range (IQR) of the given data set is 52. Values lower than 38 - 1.5(52) = -35 and higher than 90 + 1.5(52) = 165 are considered outliers.