Question

In: Statistics and Probability

If Q1, the first quartile is 200, and Q3, the third quartile, is 240: a. What...

If Q1, the first quartile is 200, and Q3, the third quartile, is 240:
a. What is the interquartile range?
b. A number in the data set would have to be above what number to be an outlier?
c. A number in the data set would have to be below what number to be an outlier?
d. Which of the following numbers are outliers? 100 150 280 330

Solutions

Expert Solution

Solution:

We are given that: Q1 = the first quartile is 200, and Q3=the third quartile, is 240.

Part a) What is the interquartile range?

Interquartile Range = IQR = Q3 - Q1

IQR = 240 - 200

IQR = 40

Part b) A number in the data set would have to be above what number to be an outlier?

Upper Bound for an outlier = Q3 + 1.5 X IQR

Upper Bound for an outlier = 240 + 1.5 X 40

Upper Bound for an outlier = 240 + 60

Upper Bound for an outlier = 300

Thus a number in the data set would have to be above 300 to be an outlier.

Part c) A number in the data set would have to be below what number to be an outlier?

Lower Bound for an outlier = Q1 - 1.5 X IQR

Lower Bound for an outlier = 200 - 1.5 X 40

Lower Bound for an outlier = 200 - 60

Lower Bound for an outlier = 140

A number in the data set would have to be below 140 to be an outlier.

Part d) Which of the following numbers are outliers? 100 150 280 330

100 is below 140, hence it is an outlier.

150 and 280 are in between lower and upper bounds, hence these two numbers are not an outliers.

330 is above upper bound 300, hence 330 is an outlier.

orchestra answered 2 years ago
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