Interquartile Range (IQR)
Interquartile Range (IQR) is a Grade 7 statistics measure in Big Ideas Math Advanced 2, Chapter 15: Probability and Statistics that quantifies the spread of the middle 50% of a data set. IQR equals Q3 minus Q1, where Q1 is the lower quartile and Q3 is the upper quartile. A larger IQR indicates greater variability in the middle portion of the data and IQR is not affected by outliers.
Key Concepts
The interquartile range (IQR) measures the spread of the middle 50% of a data set. To find the IQR: 1. Find Q1 (the median of the lower half of the data) 2. Find Q3 (the median of the upper half of the data) 3. Calculate: IQR = Q3 Q1.
Common Questions
What is the Interquartile Range (IQR)?
IQR measures the spread of the middle 50% of data by calculating the difference between the third quartile Q3 and the first quartile Q1: IQR equals Q3 minus Q1.
How do you calculate the IQR?
First find Q1 (median of the lower half) and Q3 (median of the upper half), then subtract: IQR equals Q3 minus Q1. For the data set {2, 5, 6, 9, 11, 14, 17}, Q1 is 5, Q3 is 14, so IQR is 9.
Why is IQR useful for comparing data sets?
IQR is not affected by outliers and measures variability in the central portion of the data. A smaller IQR means data is tightly clustered around the median; a larger IQR indicates more spread.
What textbook covers IQR in Grade 7?
Big Ideas Math Advanced 2, Chapter 15: Probability and Statistics covers Interquartile Range as a measure of variability.