What is the lower quartile in a cumulative frequency graph?

The lower quartile in a cumulative frequency graph is the value below which 25% of the data falls.

In a cumulative frequency graph, data is represented in a way that shows the running total of frequencies up to each data point. To find the lower quartile (also known as the first quartile or Q1), you need to identify the point where 25% of the data lies. This is done by first determining the total number of data points, then calculating 25% of this total.

For example, if you have 100 data points, 25% of 100 is 25. You then look at the cumulative frequency graph to find the value corresponding to a cumulative frequency of 25. This value is the lower quartile. If the cumulative frequency graph is plotted correctly, you can draw a horizontal line from the cumulative frequency of 25 to the curve, and then drop a vertical line down to the x-axis to find the corresponding data value.

Understanding the lower quartile is important because it helps you to analyse the spread and distribution of your data. It gives you a sense of where the lower 25% of your data lies, which can be useful in various statistical analyses, such as identifying outliers or understanding the overall distribution pattern.