Question

1. data set: 45,62,72,45,62,72

median = __ upper quartile = lower quartile = __
iqr = ____

Explanation:

Step1: Arrange data in ascending order

45, 45, 62, 62, 72, 72

Step2: Calculate the median

Since there are 6 data - points (an even number of data - points), the median is the average of the 3rd and 4th ordered values. Median=$\frac{62 + 62}{2}=62$

Step3: Calculate the lower half and upper half of data

The lower half is 45, 45, 62 and the upper half is 62, 72, 72

Step4: Calculate the lower quartile (Q1)

For the lower half (an odd - numbered set), the lower quartile is the middle value of the lower half. Q1 = 45

Step5: Calculate the upper quartile (Q3)

For the upper half (an odd - numbered set), the upper quartile is the middle value of the upper half. Q3 = 72

Step6: Calculate the inter - quartile range (IQR)

IQR=Q3 - Q1=72 - 45 = 27

Answer:

Median = 62
Upper Quartile = 72
Lower Quartile = 45
IQR = 27