Finding the Interquartile Range (IQR)
Finding the Interquartile Range (IQR) is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 9: Statistical Measures. The IQR measures the spread of the middle 50% of data and is calculated as IQR = Q3 - Q1. For a data set with Q1 = 10 and Q3 = 25, IQR = 15. Unlike the range (maximum minus minimum), the IQR is resistant to outliers because it focuses only on the central half of the data. The IQR is used to construct box plots and identify statistical outliers in Grade 6 statistics.
Key Concepts
Property The interquartile range (IQR) is the difference between the third quartile ($Q 3$) and the first quartile ($Q 1$). $$IQR = Q 3 Q 1$$.
Examples For a data set with a first quartile of $Q 1 = 10$ and a third quartile of $Q 3 = 25$, the interquartile range is $25 10 = 15$. If the quartiles of a data set are $Q 1 = 38.5$ and $Q 3 = 52$, the interquartile range is $52 38.5 = 13.5$.
Explanation The interquartile range, or IQR, measures the spread of the middle half of your data. To find the IQR, you first need to identify the first quartile ($Q 1$) and the third quartile ($Q 3$). The IQR is then calculated by simply subtracting the value of $Q 1$ from the value of $Q 3$. This value represents the range of the central 50% of the data and is less sensitive to extreme values, or outliers, than the total range.
Common Questions
What is the interquartile range (IQR)?
The IQR is the difference between the third quartile (Q3) and first quartile (Q1): IQR = Q3 - Q1. It measures the spread of the middle 50% of data values, making it a robust indicator of variability that is not affected by extreme outliers.
How do you calculate the IQR?
First find Q1 (median of lower half) and Q3 (median of upper half). Then subtract: IQR = Q3 - Q1. Example: Q1 = 38.5, Q3 = 52 → IQR = 52 - 38.5 = 13.5.
What is the difference between range and IQR?
Range = maximum - minimum, measuring total spread. IQR = Q3 - Q1, measuring the spread of only the middle 50%. IQR is more useful because extreme values (outliers) heavily inflate the range but don't affect the IQR.
Why is IQR resistant to outliers?
The IQR only looks at the middle half of data (from Q1 to Q3), ignoring the bottom 25% and top 25% where outliers typically occur. A single extreme value can dramatically change the range but has no effect on the IQR.
When do Grade 6 students learn about the IQR?
The IQR is covered in Big Ideas Math, Course 1, Chapter 9: Statistical Measures, as part of Grade 6 statistics work on measures of variability alongside mean absolute deviation.
How is the IQR used in statistics?
The IQR is used to construct box plots (the box spans from Q1 to Q3, with length = IQR), identify outliers (values more than 1.5 × IQR above Q3 or below Q1 are considered outliers), and compare the spread of different data sets.