Quartile

Definition

Quartiles are positional measures that divide a data set into four equal parts. Each quartile contains 25% of the data points arranged in ascending order. They are used to measure the spread and central tendency of data, helping in understanding the distribution characteristics.

1. First Quartile (Q1): The value below which 25% of the data lies. It is also known as the lower quartile.
2. Second Quartile (Q2): The median, the value below which 50% of the data lies.
3. Third Quartile (Q3): The value below which 75% of the data lies. It is also known as the upper quartile.
4. Fourth Quartile (Q4): The upper extreme of the data set, technically represented by the highest value in the data.

Examples

Example 1

Given the data set: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

• Q1 = 2.5
• Q2 (Median) = 5.5
• Q3 = 7.5

Example 2

For the data set: [12, 15, 14, 11, 18, 17, 16, 19, 13, 20] (sorted: [11, 12, 13, 14, 15, 16, 17, 18, 19, 20])

• Q1 = 13
• Q2 (Median) = 15.5
• Q3 = 18

Frequently Asked Questions (FAQs)

Q1: What is the purpose of calculating quartiles?

• A1: Quartiles are used to understand the spread and distribution of a data set. They help identify the central tendency and the range within which the majority of data points fall.

Q2: How are quartiles different from percentiles?

• A2: Quartiles and percentiles are both measures that describe the distribution of data. Quartiles divide the data into four equal parts, while percentiles divide the data into 100 equal parts.

Q3: Can quartiles be used for non-numeric data?

• A3: Quartiles are generally used for numeric data. Non-numeric data that can be ordered or ranked may also be divided into quartiles, but it is less common.

Q4: What is the Interquartile Range (IQR)?

• A4: The Interquartile Range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). It measures the spread of the middle 50% of the data.

Q5: How do you calculate quartiles for a data set with an even number of observations?

• A5: For an even number of observations, find the median as the average of the two middle numbers for Q2, and then determine the medians of the two halves for Q1 and Q3.

Related Terms

• Percentile: A measure indicating the value below which a given percentage of observations fall. For example, the 25th percentile is equivalent to the first quartile.
• Median: The middle value of a data set when it is ordered in ascending or descending order. It is also known as the second quartile (Q2).
• Interquartile Range (IQR): A measure of statistical dispersion representing the difference between the first quartile (Q1) and the third quartile (Q3).
• Decile: Dividing a data set into ten equal parts, each containing 10% of the data points.
• Box Plot: A graphical representation using quartiles to depict groups of numerical data through their quartiles.

Online References

1. Investopedia: Understanding Quartiles
2. Khan Academy: Quartiles and Boxplots
3. Wikipedia: Quartile

Suggested Books for Further Studies

1. “Statistics for Business and Economics” by Paul Newbold, William L. Carlson, and Betty Thorne.
2. “Probability and Statistics for Engineers and Scientists” by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, and Keying Ye.
3. “The Basic Practice of Statistics” by David S. Moore, William I. Notz, and Michael A. Fligner.

Fundamentals of Quartile: Statistics Basics Quiz

Thank you for exploring quartile-based concepts in statistics and participating in our fundamentals quiz. Continuous learning is key to mastering statistical analysis!