Math Problem Statement

What does the interquartile range (IQR) measure?
* 1 point The square root of the variance The average deviation from the mean The range of the middle 50% of the data The difference between the maximum and minimum values

Solution

The interquartile range (IQR) measures:

The range of the middle 50% of the data.

The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), i.e., IQR = Q3 - Q1. It is a measure of statistical dispersion that shows the spread of the middle half of a dataset, effectively filtering out outliers and providing a more robust understanding of data variability.


Would you like more details or have any questions? Here are some related questions:

  1. How do you calculate the first and third quartiles of a dataset?
  2. Why is the interquartile range a better measure of spread than the range?
  3. How does the IQR help identify outliers in a dataset?
  4. What is the relationship between IQR and box plots?
  5. Can the IQR be negative? Why or why not?

Tip: The IQR is especially useful when comparing the spread of different datasets, as it is not affected by extreme values or outliers.

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Math Problem Analysis

Mathematical Concepts

Statistics
Interquartile Range (IQR)
Data Dispersion

Formulas

IQR = Q3 - Q1

Theorems

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Suitable Grade Level

Grades 8-10