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Chapter 2: Q. 2.13 (page 89)

For the following 11salaries, calculate the IQR and determine if any salaries are outliers. The salaries are in

dollars.
role="math" localid="1647875427889" \(33,000;\)64,500;\(28,000;\)54,000;\(72,000;\)68,500;\(69,000;\)42,000;\(54,000;\)120,000;$40,500

Short Answer

Expert verified
We can tell whether or not there is an outlier in the data using the IQR.
We call 120000an outlier since it falls outside of the IQR's acceptable range.

Step by step solution

01

Given

Here we have salaries$33,000;$64,500;$28,000;$54,000;$72,000;$68,500;$69,000;$42,000;$54,000;$120,000;$40,500

02

Explanation

The IQR of the 11salaries and which salaries is the outlier.

We get Q1=40500;Q3=69000;

IQR=Q3-Q1=28500

1.5*鈭�QR=42750

So a observation will called outlier if it less than lower limit of Q1-1.5*鈭�QR=-2250

And beyond Q3+1.5*lQR=111750So, only one observation is beyond highest limit which is $120000. Hence this is outlier.

The rule of thumb for obtaining IQRQ3-Q1=28500. The IQR was used to identify data outliers.
To define outlier, we evaluated bottom and upper boundaries. After taking into account the intervals, we get at 120000, which is above the top limit.

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