How to Find the First and Third Quartiles?

To find the first and third quartiles (Q1 and Q3) of a dataset, you can follow these steps:

1.Arrange the Data in Ascending Order:

• If the dataset is not already sorted, arrange it in ascending order from smallest to largest.

2.Calculate the Median (Q2):

• Find the median of the dataset, which is also the second quartile (Q2). If the dataset has an odd number of observations, the median is the middle value. If it has an even number of observations, the median is the average of the two middle values.

3.Calculate Q1 (First Quartile):

• Q1 is the median of the lower half of the dataset. If the dataset has an odd number of observations, it excludes the median (Q2) and includes the values below it. If it has an even number of observations, it includes the median (Q2) and the values below it. Calculate the median of this lower half to find Q1.

4.Calculate Q3 (Third Quartile):

• Q3 is the median of the upper half of the dataset. If the dataset has an odd number of observations, it excludes the median (Q2) and includes the values above it. If it has an even number of observations, it includes the median (Q2) and the values above it. Calculate the median of this upper half to find Q3.

In summary, the steps are:

• Arrange the data in ascending order.
• Find the median (Q2).
• For Q1, find the median of the lower half of the dataset.
• For Q3, find the median of the upper half of the dataset.

It's important to note that there are different methods for calculating quartiles, and some statistical software may use slightly different approaches. The method described above is one common approach known as the "Tukey method."