Chapter 2: Q. 2.13 (page 89)

For the following $11$ salaries, 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

120000

an outlier since it falls outside of the IQR's acceptable range.

Step by step solution

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$

Explanation

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

We get $Q 1 = 40500; Q 3 = 69000;$

$IQR = Q_{3} - Q_{1} = 28500$

$1 . 5^{*} ∣ Q R = 42750$

So a observation will called outlier if it less than lower limit of $Q_{1} - 1 . 5^{*} ∣ Q R = - 2250$

And beyond $Q_{3} + 1 . 5^{*} lQR = 111750$ So, only one observation is beyond highest limit which is $$ 120000$ . Hence this is outlier.

The rule of thumb for obtaining

I Q R Q_{3} - Q_{1} = 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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For the following $11$ salaries, 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

Step by step solution

Given

Explanation

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

Step by step solution

Given

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

For the following $11$ salaries, 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$