Compare Data Sets Using Centre And Spread
Overview
To compare two groups fairly, one number is rarely enough. You need a measure of the center (where the data sits) and a measure of the spread (how varied it is). Only together do they tell the full story.
In this lesson you will compare data sets using a measure of center (mean or median) and a measure of spread (range or interquartile range), drawing clear conclusions about how two groups differ.
Objectives
- Compare two data sets using measures of center (median, mean) and spread, and the shape of the distribution.
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Lesson Evaluation
Congratulations on completing the lesson on Compare Data Sets Using Centre And Spread. 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.
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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.
- To compare two data sets fairly you should use: A. only an average B. only the range C. a measure of center and a measure of spread D. only the mode Answer: C
- Class A scores 5,5,5,5,5 and Class B scores 1,3,5,7,9. The means are: A. different B. both 5 C. both 3 D. both 9 Answer: B
- The range of Class B (1,3,5,7,9) is: A. 0 B. 5 C. 8 D. 9 Answer: C
- Two data sets with the same mean but different spreads are: A. identical B. equally consistent C. different in how varied they are D. impossible Answer: C
- A smaller spread means the data is: A. larger on average B. more consistent C. less reliable D. higher Answer: B
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Recommended Books
Further learning from open sources
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Textbook section
Measures of the Spread of the Data
An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard devia
"Introductory Statistics: Measures of the Spread 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/2-7-measures-of-the-spread-of-the-data. Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
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Textbook section
Skewness and the Mean, Median, and Mode
Consider the following data set. 4; 5; 6; 6; 6; 7; 7; 7; 7; 7; 7; 8; 8; 8; 9; 10 This data set can be represented by following histogram. Each interval has width one, and each value is located in the middle of an interval. The histogram displays a symmetrical distribution of data. A distribution is
"Introductory Statistics: Skewness and the Mean, Median, and Mode" 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/2-6-skewness-and-the-mean-median-and-mode. 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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