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.

Solution

The given statement is false.

An outlier is not just any number above Q3Q_3 (upper quartile) or below Q1Q_1 (lower quartile). The correct definition involves the interquartile range (IQR).

Corrected Statement:

An outlier is any number greater than Q3+1.5×IQRQ_3 + 1.5 \times IQR or less than Q11.5×IQRQ_1 - 1.5 \times IQR, where IQR=Q3Q1IQR = Q_3 - Q_1.

Would you like further explanation or have any questions on this topic?

Related Questions:

  1. What is the interquartile range (IQR)?
  2. How do you calculate the first and third quartiles?
  3. Why are outliers important in data analysis?
  4. What are the effects of outliers on statistical measures like mean and median?
  5. How does the 1.5 rule for outliers relate to the spread of data?

Tip:

When identifying outliers, remember that extreme values can significantly affect statistical results, especially in small datasets.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Outliers
Quartiles
Interquartile Range (IQR)

Formulas

IQR = Q3 - Q1
Outlier above: Q3 + 1.5 * IQR
Outlier below: Q1 - 1.5 * IQR

Theorems

Interquartile Range Theorem for Outliers

Suitable Grade Level

Grades 9-12