Question

J.D. Powers and Associates surveyed cell phone users in order to learn about the minutes of cell phone usage per month. Minutes per month for a sample of 15 cell phone users are shown here. What is the interquartile range (IQR) of the data set?

30   135      180      210      245     

250      265      380      395      420     

430      615      690      830 880

Answer 1

Interquartile Range represents the middle 50% of the data set.

Mathematically,

It is the difference between the third quartile and the first quartile.

For calculation of the third quartile we use:

for the first quartile we use:

where "N" represents the total number of observations.

30
135
180
210 1st Quartile
245
250
265
380  Median
395
420
430
615 3rd Quartile
690
830
880

We have a total of 15 observations.

So, , the third quartile is the middle observation of the upper half of the data.

Thus, 12th observation would represent the third quartile which is 615

, the first quartile is the middle observation of the lower half of the data.

Thus, 4th observation would represent the first quartile which is 210.

Thus,

.

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