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:
- Start with the frequency of the first interval 9.
- 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 at20onthecumulativefrequencyaxis
- Lower Quartile: 41 cm at10onthecumulativefrequencyaxis
- Upper Quartile: 53 cm at30onthecumulativefrequencyaxis
- 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.
