Quartiles

Quartiles are values that divide a data set into four equal parts. There are three quartiles, denoted as Q1, Q2, and Q3. Q2 is the same as the median, and it divides the data set into two halves. Q1 divides the lower half of the data (excluding Q2), and Q3 divides the upper half of the data (excluding Q2).

Finding Quartiles

To find the quartiles of a data set, you can follow these steps:

1. First, arrange the data in ascending order.
2. Find the median (Q2) of the data set.
3. To find Q1, calculate the median of the lower half of the data set (the values below Q2).
4. To find Q3, calculate the median of the upper half of the data set (the values above Q2).

Example

Consider the following data set: 12, 15, 17, 20, 22, 25, 30, 35, 40, 45

First, arrange the data in ascending order: 12, 15, 17, 20, 22, 25, 30, 35, 40, 45

The median (Q2) is the middle value, which is 22.

The lower half of the data set is 12, 15, 17, 20, so the median of the lower half (Q1) is 16.

The upper half of the data set is 25, 30, 35, 40, 45, so the median of the upper half (Q3) is 35.

Usage of Quartiles

Quartiles are used to understand the spread and distribution of a data set. They are particularly helpful when comparing different sets of data. For example, comparing the quartiles of two different test scores can help identify the differences in the performance of the students.

Understanding quartiles is important in various statistical analyses and helps in making informed decisions based on data distribution.

It's important for students to practice calculating quartiles with different data sets to gain a strong understanding of the concept.

Remember, Q1 is the 25th percentile, Q2 is the 50th percentile (median), and Q3 is the 75th percentile.

Now that you understand quartiles, it's time to practice and master the concept through various problems and exercises.