Cumulative Frequency Diagrams
Overview
A cumulative frequency diagram adds up frequencies as you go, building a smooth rising curve that reveals the median and the spread of a data set at a glance. It is the key to reading quartiles and percentiles from grouped data.
In this lesson (Extended tier) you will draw and interpret cumulative frequency tables and diagrams, and estimate the median, quartiles, percentiles and interquartile range from the curve.
Objectives
- Draw and interpret cumulative frequency tables and diagrams.
- Estimate and interpret the median, percentiles, quartiles and interquartile range from cumulative frequency diagrams.
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Lesson Evaluation
Congratulations on completing the lesson on Cumulative Frequency Diagrams. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- Cumulative frequency points are plotted at the: A. middle of each group B. upper boundary of each group C. lower boundary D. frequency value Answer: B
- For 40 values, the median is read across from a cumulative frequency of: A. 10 B. 20 C. 30 D. 40 Answer: B
- The lower quartile of n values is read from a cumulative frequency of: A. n/4 B. n/2 C. 3n/4 D. n Answer: A
- If LQ = 11 and UQ = 17, the interquartile range is: A. 6 B. 11 C. 17 D. 28 Answer: A
- A cumulative frequency curve is typically: A. a straight line B. a rising S-shape C. a parabola D. a falling line Answer: B
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Recommended Books
Further learning from open sources
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Textbook section
Measures of the Location of the Data
The common measures of location are quartiles and percentiles Quartiles are special percentiles. The first quartile, Q 1 , is the same as the 25 th percentile, and the third quartile, Q 3 , is the same as the 75 th percentile. The median, M , is called both the second quartile and the 50 th percenti
"Introductory Statistics: Measures of the Location of the Data" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/introductory-statistics/pages/2-3-measures-of-the-location-of-the-data. Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
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Textbook section
Frequency, Frequency Tables, and Levels of Measurement
Once you have a set of data, you will need to organize it so that you can analyze how frequently each datum occurs in the set. However, when calculating the frequency, you may need to round your answers so that they are as precise as possible. A simple way to round off answers is to carry your final
"Introductory Statistics: Frequency, Frequency Tables, and Levels of Measurement" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/introductory-statistics/pages/1-3-frequency-frequency-tables-and-levels-of-measurement. Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
Published by other organisations under open licences, credited as they ask. Links open their websites.
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