Data about cell phone usage was collected from 14 different people. The list shows the number of incoming calls each person received during the month of August.
87, 102, 131, 132, 155, 173, 178, 204, 211, 244, 253, 278, 301, 371
What is the interquartile range of the data?
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3).
Step 1: Arrange the data in ascending order:
87, 102, 131, 132, 155, 173, 178, 204, 211, 244, 253, 278, 301, 371
Step 2: Find the median of the data set, which is the middle value:
Median = (173 + 178) / 2 = 175.5
Step 3: Find the first quartile (Q1), which is the median of the lower half of the data set:
Lower half: 87, 102, 131, 132, 155, 173
Q1 = (131 + 132) / 2 = 131.5
Step 4: Find the third quartile (Q3), which is the median of the upper half of the data set:
Upper half: 204, 211, 244, 253, 278, 301, 371
Q3 = (253 + 278) / 2 = 265.5
Step 5: Calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 265.5 - 131.5
IQR = 134
Therefore, the interquartile range of the data is 134.