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 Q1Q_1 is 58.0.
  • The second quartile Q2Q_2 (the median) is 59.0.
  • The third quartile Q3Q_3 is 61.5.

Part 2: Interquartile Range (IQR)

  • The interquartile range (IQR) is Q3Q1=61.558.0=3.5Q_3 - Q_1 = 61.5 - 58.0 = 3.5.

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:

  1. How are quartiles calculated in different distributions?
  2. What is the significance of the interquartile range (IQR)?
  3. How do outliers affect statistical analysis?
  4. Can a data set have multiple outliers, and how do we handle them?
  5. 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.

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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