Question
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Use the accompanying data set to complete the following actions.
a. Find the quartiles.
b. Find the interquartile range.
c. Identify any outliers.
585662555456596463655855586381 ,
a. Find the quartiles.
The first quartile, , is 56 .
The second quartile, , is 62 .
The third quartile, , is 63 .
(Type integers or decimals.)

Ask by Rodriquez O'Quinn. in the United States
Jan 10,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

  • Interquartile Range (IQR): 7
  • Outlier: 81

Solution

Sure, let’s continue with parts b and c based on your dataset and the quartiles you’ve identified.

b. Find the Interquartile Range (IQR)

The Interquartile Range (IQR) is a measure of statistical dispersion and is calculated as the difference between the third quartile ( ) and the first quartile ( ).
Given:
Interquartile Range (IQR) = 7

c. Identify Any Outliers

Outliers are data points that fall significantly below or above the overall pattern of the data. To identify outliers, we can use the 1.5*IQR rule:
  1. Calculate the Lower Bound:
  2. Calculate the Upper Bound:
  3. Determine Outliers:
    • Any data point less than 45.5 or greater than 73.5 is considered an outlier.
Given Data Set:
Checking for Outliers:
  • The data point 81 is greater than 73.5, so it is an outlier.
Identified Outlier:
  • 81

Summary

  • Interquartile Range (IQR): 7
  • Outlier Detected: 81
If you have any further questions or need additional assistance, feel free to ask!

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

Mind Expander

The interquartile range (IQR) can be found by subtracting the first quartile from the third quartile: . With the values provided, we calculate: .
To identify outliers, you can use the 1.5 times the IQR rule. Any number below or above is an outlier. Here, that means any number below (45.5) or above (73.5) would be considered an outlier. Thus, in this dataset, there aren’t any outliers since all values fall within this range!

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