Math Problem Statement

Determine whether the statement is true or false. If it is false rewrite it as a true statement

An outlier is any number above

Upper Q 3Q3

or below

Upper Q 1Q1.

Question content area bottom

Part 1

A.

This statement is false. A true statement is​ "An outlier is any number above

Upper Q 3Q3plus+​1.5(IQR)

or below

Upper Q 1Q1minus−​1.5(IQR)

are considered​ outliers."

B.

This statement is false. A true statement is​ "An outlier is any number above

Upper Q 1Q1minus−​1.5(IQR)

or below

Upper Q 3Q3plus+​1.5(IQR)."

C.

This statement is false. A true statement is​ "An outlier is any number above

2 times Upper Q 32•Q3

or below

2 times Upper Q 12•Q1​."

D.

This statement is true.

Solution

The correct answer is A.

The given statement is false because it does not account for the proper definition of outliers using the interquartile range (IQR).

A true statement would be:
"An outlier is any number above Q3 + 1.5(IQR) or below Q1 - 1.5(IQR)."

Here’s a breakdown:

  • Q1 (Lower Quartile): The median of the lower half of the dataset.
  • Q3 (Upper Quartile): The median of the upper half of the dataset.
  • IQR (Interquartile Range): The range between Q1 and Q3, i.e., IQR=Q3Q1IQR = Q3 - Q1.

Outliers are numbers that lie outside the range: [Q11.5(IQR),Q3+1.5(IQR)][Q1 - 1.5(IQR), Q3 + 1.5(IQR)]

This rule helps in identifying extreme values in the dataset.

Would you like to know more about interquartile ranges and how they are used in statistics?

Here are some related questions:

  1. How is the interquartile range (IQR) calculated?
  2. What is the significance of identifying outliers in a dataset?
  3. How do Q1 and Q3 relate to the overall spread of data?
  4. What are some common methods to handle outliers?
  5. Can outliers be beneficial in any statistical analysis?

Tip: Outliers can skew data distributions and affect statistical measures like mean and standard deviation, so it's crucial to understand how they impact your analysis.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Outliers
Interquartile Range (IQR)

Formulas

Outliers: Q3 + 1.5(IQR) or Q1 - 1.5(IQR)
IQR = Q3 - Q1

Theorems

Interquartile Range (IQR) method for detecting outliers

Suitable Grade Level

Grades 9-12