How to Finding Range, Quartile and Interquartile Range

Once you know the mean, median, and mode, the next step in statistical analysis is measuring spread — how tightly or loosely the data is clustered. The range, quartiles, and interquartile range (IQR) are the key spread measures you need for the GED Math test. They also form the backbone of box-and-whisker plots.

What Are Range, Quartiles, and IQR?

• Range = \(\color{blue}{\text{ Maximum } – \text{ Minimum }}\)   (total spread)
• Q1 \(\color{blue}{(\text{ First Quartile }) = \text{ median }}\) of the lower half of the data (25th percentile)
• Q2 \(\color{blue}{(\text{ Second Quartile }) = \text{ median }}\) of the entire data set (50th percentile)
• Q3 \(\color{blue}{(\text{ Third Quartile }) = \text{ median }}\) of the upper half of the data (75th percentile)
• IQR = \(\color{blue}{Q3 – Q1}\)   (spread of the middle 50% of the data)

How to Find Quartiles and IQR

Step-by-Step Method

1. Sort the data from least to greatest.
2. Find the median (Q2): this is the middle value (or average of two middle values for even count).
3. Find Q1: find the median of all values below Q2.
4. Find Q3: find the median of all values above Q2.
5. Compute \(\color{blue}{\text{ IQR } = Q3 – Q1}\).

Key Notes

• If the data set has an odd number of values, exclude the median when finding Q1 and Q3.
• IQR represents the range of the “middle half” of the data and is more resistant to outliers than the full range.

Step-by-Step Summary

1. Sort the data.
2. \(\color{blue}{\text{ Range } = \text{ max } – \text{ min }}\).
3. \(\color{blue}{Q2 = \text{ median }}\) of the full data set.
4. \(\color{blue}{Q1 = \text{ median }}\) of the lower half; \(\color{blue}{Q3 = \text{ median }}\) of the upper half.
5. \(\color{blue}{\text{ IQR } = Q3 – Q1}\).

Watch: Interquartile Range (IQR) (Video Lesson)

Math with Mr. J walks through finding the IQR with step-by-step examples:

GED Math for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the GED Math Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.33 out of 5 based on 105 customer ratings

Satisfied 91 Students

Worked Examples

Example 1: Find the range, Q1, Q3, and IQR of: 4, 7, 10, 12, 15, 18, 20.

Sorted: 4, 7, 10, 12, 15, 18, 20
\(\color{blue}{\text{ Range } = 20 – 4}\) = 16
Q2 \(\color{blue}{(\text{ median }) = 12}\) (4th of 7)
Lower half: 4, 7, 10 → \(\color{blue}{Q1 = \frac{(7+10)}{2}}\) = 8.5
Upper half: 15, 18, 20 → \(\color{blue}{Q3 = \frac{(15+18)}{2}}\) = 16.5
\(\color{blue}{\text{ IQR } = 16.5 – 8.5}\) = 8

Example 2: Find the IQR of: 2, 5, 6, 8, 10, 11, 14, 16.

\(\color{blue}{Q1 = \frac{(5+6)}{2} = 5.5}\); \(\color{blue}{Q3 = \frac{(11+14)}{2} = 12.5}\)
\(\color{blue}{\text{ IQR } = 12.5 – 5.5}\) = 7

Example 3: A data set has \(\color{blue}{Q1 = 20}\) and \(\color{blue}{Q3 = 35}\). What is the IQR?

\(\color{blue}{\text{ IQR } = 35 – 20}\) = 15

Example 4: Scores: 60, 65, 70, 75, 80, 85, 90, 95. Find Q1, Q3, and IQR.

\(\color{blue}{Q1 = \frac{(65+70)}{2} = 67.5}\); \(\color{blue}{Q3 = \frac{(85+90)}{2} = 87.5}\)
\(\color{blue}{\text{ IQR } = 87.5 – 67.5}\) = 20

More Practice: Calculating IQR (Video)

Khan Academy’s 6th-grade data and statistics lesson explains the IQR with visual dot-plot examples:

Exercises

1. Find the range of: 13, 27, 5, 41, 9, 33, 18.
2. Find Q1, Q3, and IQR of: 3, 6, 7, 9, 12, 15, 18, 21.
3. A data set has \(\color{blue}{\text{ range } = 30}\) and \(\color{blue}{\text{ min } = 12}\). What is the max?
4. Find the IQR of: 10, 20, 30, 40, 50.
5. Data: 1, 4, 6, 8, 10, 12, 14. Find Q1, Q3, IQR, and range.
6. If \(\color{blue}{Q1 = 15}\) and \(\color{blue}{\text{ IQR } = 12}\), what is Q3?

Answers

1. \(\color{blue}{41 – 5}\) = 36
2. \(\color{blue}{Q1=\frac{(6+7)}{2}=6.5}\); \(\color{blue}{Q3=\frac{(15+18)}{2}=16.5}\); IQR=10
3. \(\color{blue}{12 + 30}\) = 42
4. Sorted: 10,20,30,40,50; \(\color{blue}{Q1=20}\); \(\color{blue}{Q3=40}\); IQR=20
5. \(\color{blue}{Q1=\frac{(4+6)}{2}=5}\); \(\color{blue}{Q3=\frac{(10+12)}{2}=11}\); IQR=6; \(\color{blue}{\text{ Range }=14-1}\)=13
6. \(\color{blue}{Q3 = 15 + 12}\) = 27

Statistics for Beginners The Ultimate Step by Step Guide to Acing Statistics

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Frequently Asked Questions

What does a small IQR mean about a data set?

A small IQR means the middle half of the data is clustered closely together — the data is relatively consistent. A large IQR means the middle half is spread out — the data has more variability.

Do I include the median when finding Q1 and Q3?

For an odd number of values, exclude the median (Q2) before splitting the data into lower and upper halves. For an even number of values, simply split the data in half without excluding any value.

How is IQR used to find outliers?

The standard rule: any value below \(\color{blue}{Q1 – 1.5 \times \text{ IQR }}\) or above \(\color{blue}{Q3 + 1.5 \times \text{ IQR }}\) is considered an outlier. This is known as Tukey’s fence method.

Related Topics

• How to Identify an Outlier
• Mean, Median, Mode, and Range
• Distributions in Line Plot
• Line Plot
• How to Solve the Frequency Distribution Table