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Learn Cumulative Frequency Graphs and Tables: Easy Examples and Fun Problems

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Libby

06/09/2023

Maths

Cumulative frequency notes

Learn Cumulative Frequency Graphs and Tables: Easy Examples and Fun Problems

Cumulative frequency graphs and tables are essential tools in statistics for understanding cumulative frequency. They help visualize and analyze data distribution, particularly useful for finding median and quartiles.

  • Cumulative frequency is the running total of frequencies up to a specific point in a dataset.
  • A cumulative frequency table organizes data by showing the cumulative totals for each category.
  • A cumulative frequency graph plots these cumulative totals against the upper boundaries of each class interval.
  • Key statistics like median and quartiles can be easily determined from these graphs.
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06/09/2023

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Learn Cumulative Frequency Graphs and Tables: Easy Examples and Fun Problems

Cumulative frequency graphs and tables are essential tools in statistics for understanding cumulative frequency. They help visualize and analyze data distribution, particularly useful for finding median and quartiles.

  • Cumulative frequencyis the running total of frequencies up to a... Show more

cumulative
The Cumulative
frequency is the
total 'so far you
add the frequencies
up to that point.
EXAMPLE
The heights of some plants
were r

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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 99.
  2. Add each subsequent frequency to the running total 9+16=25,25+12=37,37+3=409 + 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 IQRIQR: The difference between the upper and lower quartiles.

Using the graph, we can determine:

  • Median: 48 cm at20onthecumulativefrequencyaxisat 20 on the cumulative frequency axis
  • Lower Quartile: 41 cm at10onthecumulativefrequencyaxisat 10 on the cumulative frequency axis
  • Upper Quartile: 53 cm at30onthecumulativefrequencyaxisat 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.

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Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

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This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

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Sudenaz Ocak

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In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

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