The median is like a ruler that divides data into two equal parts, right in the middle (50%). Well, there's another friend of the median, called quartiles.
If the median divides data into two, quartiles are even better; they divide the sorted data into four equal parts! Imagine you have a chocolate bar, and you break it into four equal pieces. Quartiles are the breaking points.
There are three quartile breaking points:
Lower Quartile (Q1): This is the first break. It separates the smallest of the data from the rest. Like the first quarter of the chocolate.
25%
Middle Quartile (Q2): This is the median! It's exactly in the middle, dividing the data in half (50% left, 50% right). Like the break in the middle of the chocolate.
Upper Quartile (Q3): This is the last break. It separates the smallest 75% of the data from the largest 25%. Like the boundary after three-quarters of the chocolate.
So, Q1, Q2, and Q3 divide our data into four small groups with the same number of data points (25% each).
If the result is a whole number, for example 5, then Q1 is the value of the 5th data point.
If the result has a decimal, for example 5.25, then Q1 lies between the 5th and 6th data points. (There's a way to calculate its value later, but for now, we're just finding the position).
Simple Example:
Suppose we have 20 data points (n=20).
The position of Q1 is the data point at 41(20+1), which is data point 421 or 5.25.
This means Q1 is between the 5th and 6th data points.
You might be wondering, "If there's Q1, Q2, and Q3, is there a Q4?"
Technically, the concept of quartiles divides the data into four parts. Q1 is the boundary for the first 25%, Q2 (the median) is the 50% boundary, and Q3 is the 75% boundary. The final boundary, which encompasses 100% of the data, is actually the maximum value of the dataset.
So, while we could refer to the maximum value as Q4, in statistical analysis, we don't typically use the term Q4 explicitly. The main focus is on Q1, Q2, and Q3 because they provide important information about the spread and center of the data in the lower, middle, and upper sections. The minimum value is sometimes called Q0, but like Q4, it's less commonly used than Q1, Q2, and Q3.
