Math Problem Statement
What does the interquartile range (IQR) measure?
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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:
- How do you calculate the first and third quartiles of a dataset?
- Why is the interquartile range a better measure of spread than the range?
- How does the IQR help identify outliers in a dataset?
- What is the relationship between IQR and box plots?
- 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
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