Understanding Cumulative Frequency

Cumulative frequency is a fundamental concept in statistics that involves adding up frequencies as you progress through a dataset. This page explores the creation and interpretation of cumulative frequency tables and graphs, along with their applications in statistical analysis.

Definition: Cumulative frequency is the total frequency "so far," calculated by adding the frequencies up to a specific point in a dataset.

The page presents an example using plant height data to illustrate the process of creating a cumulative frequency table and graph.

Example: Heights of plants were recorded in centimeter intervals:

• 30 < h ≤ 40: 9 plants
• 40 < h ≤ 50: 16 plants
• 50 < h ≤ 60: 12 plants
• 60 < h ≤ 70: 3 plants

To create a cumulative frequency table:

1. Start with the frequency of the first interval (9).
2. Add each subsequent frequency to the running total (9 + 16 = 25, 25 + 12 = 37, 37 + 3 = 40).

The resulting cumulative frequency table:

• 30 < h ≤ 40: 9
• 30 < h ≤ 50: 25
• 30 < h ≤ 60: 37
• 30 < h ≤ 70: 40

Highlight: When creating a cumulative frequency graph, plot points using the upper boundary of each height interval and its corresponding cumulative frequency.

The cumulative frequency graph is then drawn by connecting these points with a smooth curve.

Vocabulary:

• Median: The middle value in a dataset, found at the halfway point on the cumulative frequency graph.
• Lower Quartile: The value at 1/4 of the way through the data.
• Upper Quartile: The value at 3/4 of the way through the data.
• Interquartile Range (IQR): The difference between the upper and lower quartiles.

Using the graph, we can determine:

• Median: 48 cm (at 20 on the cumulative frequency axis)
• Lower Quartile: 41 cm (at 10 on the cumulative frequency axis)
• Upper Quartile: 53 cm (at 30 on the cumulative frequency axis)
• Interquartile Range: 53 - 41 = 12 cm

Highlight: The cumulative frequency graph allows for quick visual estimation of these important statistical measures, making it a valuable tool for data analysis and interpretation.