How do you find the quartiles on a graph?

To find quartiles on a graph, particularly from a cumulative frequency curve, you locate specific percentage points on the y-axis and then read the corresponding data values from the x-axis. This method visually determines the data points that divide your dataset into four equal parts.

Understanding Quartiles and Cumulative Frequency Curves

Quartiles are values that divide a dataset into four equal segments. They are:

• Q1 (Lower Quartile): The value below which 25% of the data falls.
• Q2 (Median): The value below which 50% of the data falls. This is also the median of the dataset.
• Q3 (Upper Quartile): The value below which 75% of the data falls.

A cumulative frequency curve (also known as an ogive) is a graph that displays the cumulative frequency against the upper class boundary of the data. The y-axis represents the cumulative frequency (or percentage), and the x-axis represents the data values. It's an ideal tool for graphically estimating quartiles, medians, and percentiles.

Step-by-Step Guide: Finding Quartiles from a Cumulative Frequency Curve

Follow these steps to accurately find the quartiles:

Step 1: Determine the Total Frequency (N)

First, identify the total number of data points in your dataset. This is typically the maximum value on the cumulative frequency (y) axis of your graph.

Step 2: Calculate Quartile Positions on the Y-axis

Once you have the total frequency (N), calculate the y-axis position for each quartile:

• Q1 (Lower Quartile): Locate the value corresponding to 25% of N (0.25 × N) on the cumulative frequency axis.
• Q2 (Median): Locate the value corresponding to 50% of N (0.50 × N) on the cumulative frequency axis.
• Q3 (Upper Quartile): Locate the value corresponding to 75% of N (0.75 × N) on the cumulative frequency axis.

Step 3: Locate on the Y-axis and Read from the X-axis

For each calculated quartile position from Step 2, perform the following actions:

1. Start on the Y-axis: "Come on the y-axis and locate" the specific cumulative frequency value for the quartile you're finding (e.g., 25% of N for Q1).
2. Go Across to the Curve: From that y-axis point, "go straight across" horizontally (parallel to the x-axis) until you intersect the cumulative frequency curve.
3. Come Down to the X-axis: From the point where your horizontal line intersects the curve, "come straight down" vertically (parallel to the y-axis) to the x-axis.
4. Read the Value: The value you read on the x-axis at this point is your quartile.

Example from Reference:

As illustrated in the provided reference for finding the third quartile (Q3):

• You would "come on the y-axis" and locate the position for 75% of the total frequency.
• If, for instance, this point is 27 on the y-axis (meaning 75% of the data falls below the Q3 value), you would "go to 27 go straight across" to the curve.
• Then, you "come straight down" to the x-axis.
• The reference states, "and then I can see 161. 2 3 4 165 is going to be my third quartile." This indicates that the value read on the x-axis for that specific cumulative frequency (27) was 165, which is the third quartile.

Key Considerations for Accuracy

• Scale of Axes: Be mindful of the scale of both the x and y axes to read values accurately.
• Straight Lines: Use a ruler or a straight edge to draw perfectly horizontal and vertical lines from the axes to the curve to minimize reading errors.
• Interpolation: As seen in the example ("161. 2 3 4 165"), you might need to interpolate between marked values on the x-axis for a precise reading.

By following these steps, you can effectively find the quartiles on a cumulative frequency curve, providing insights into the spread and distribution of your data.