Math Problem Statement
Use the accompanying data set to complete the following actions.
a. Find the quartiles.
b. Find the interquartile range.
c. Identify any outliers.
57 61 62 58 59 55 61 58 63 58 61 59 64 57 73
Question content area bottom
Part 1
a. Find the quartiles.
The first quartile, Upper Q 1, is
enter your response here.
The second quartile, Upper Q 2, is
enter your response here.
The third quartile, Upper Q 3, is
enter your response here.
(Type integers or decimals.)
Part 2
b. Find the interquartile range.
The interquartile range (IQR) is
enter your response here. (Type an integer or a decimal.)
Part 3
c. Identify any outliers.
Choose the correct answer below.
A.
There exists at least one outlier in the data set at
73.
(Use a comma to separate answers as needed.)
B.
There are no outliers in the data set.
Solution
Part 1: Quartiles
- The first quartile is 58.0.
- The second quartile (the median) is 59.0.
- The third quartile is 61.5.
Part 2: Interquartile Range (IQR)
- The interquartile range (IQR) is .
Part 3: Outliers
- The only outlier in the data set is 73, as it exceeds the upper bound.
Would you like more details or further clarification on any part? Here are five related questions:
- How are quartiles calculated in different distributions?
- What is the significance of the interquartile range (IQR)?
- How do outliers affect statistical analysis?
- Can a data set have multiple outliers, and how do we handle them?
- What are other methods for detecting outliers besides IQR?
Tip: Outliers can significantly skew the results of statistical analysis. Always consider them when summarizing data.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Descriptive Statistics
Quartiles
Interquartile Range
Outliers
Formulas
First Quartile (Q1) = (n+1)th data point / 4
Second Quartile (Median) = Middle value of the data set
Third Quartile (Q3) = 3(n+1)th data point / 4
Interquartile Range (IQR) = Q3 - Q1
Outliers: Values < Q1 - 1.5 * IQR or > Q3 + 1.5 * IQR
Theorems
Quartile Theorem
Outlier Detection using IQR
Suitable Grade Level
Grades 9-12
Related Recommendation
Quartiles, Interquartile Range, and Outliers for Data Set
Quartiles, IQR, and Outliers for Data Set 54, 59, 61, 59, 57, 55, 62, 61, 57, 59, 55, 61, 64, 56, 74
Calculating Quartiles, Interquartile Range, and Outliers for a Data Set
Quartiles and Outliers Calculation for Data Set 39 to 92
Finding Quartiles, IQR, and Outliers from a Data Set