Understanding the Lower Quartile: A Step-by-Step Guide to Calculating and Interpreting Data

The Lower Quartile

The lower quartile, also known as the first quartile (Q1), is a statistical measure that divides a data set into four equal parts

The lower quartile, also known as the first quartile (Q1), is a statistical measure that divides a data set into four equal parts. It represents the data point below which 25% of the data values lie.

To find the lower quartile, follow these steps:

Step 1: Sort the data in ascending order.

Step 2: Determine the position of the lower quartile. This can be done by using the formula (n+1)/4, where n represents the total number of data points.

Step 3: If the position is a whole number, then the lower quartile is the data value at that position. If the position is a decimal, round it up to the nearest whole number and find the data value at that position.

Let’s illustrate this with an example:

Example:
Consider the following data set: 10, 20, 25, 30, 35, 40, 50, 55, 60, 65, 70, 80, 85, 90

Step 1: Sort the data in ascending order: 10, 20, 25, 30, 35, 40, 50, 55, 60, 65, 70, 80, 85, 90

Step 2: Determine the position of the lower quartile: (14+1)/4 = 3.75

Step 3: Since the position is a decimal, round it up to the nearest whole number: 4

The lower quartile is the value at the 4th position, which is 30.

Therefore, in this example, the lower quartile is 30. This means that 25% of the data values are less than or equal to 30.

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