Math Problem Statement

Based on the following calculator output, determine the inter-quartile range of the dataset.

Solution

The interquartile range (IQR) is calculated as the difference between the third quartile (Q3Q_3) and the first quartile (Q1Q_1).

From the image:

  • Q3=140Q_3 = 140
  • Q1=116Q_1 = 116

IQR=Q3Q1=140116=24\text{IQR} = Q_3 - Q_1 = 140 - 116 = 24

The interquartile range of the dataset is 24.

Would you like an explanation of how interquartile range helps measure spread in data?

Here are 5 related questions for you to consider:

  1. What is the purpose of the interquartile range in statistics?
  2. How is the interquartile range used to identify outliers in a dataset?
  3. What is the difference between the interquartile range and the standard deviation?
  4. How do you calculate Q1Q_1 and Q3Q_3 for a larger dataset?
  5. Why might the interquartile range be more robust than the range?

Tip: Always verify that your Q1Q_1 and Q3Q_3 values are correct, as they directly affect the IQR calculation.

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Math Problem Analysis

Mathematical Concepts

Interquartile Range
Quartiles
Data Spread

Formulas

IQR = Q3 - Q1

Theorems

None directly, but based on descriptive statistics concepts.

Suitable Grade Level

Grades 8-12