Statistical Measures
Overview
Statistical measures let you summarise a data set with a single representative value and describe how spread out the data is. The mean, median and mode each capture a different sense of 'average', while the range and interquartile range tell you how much the values vary. Together they turn raw numbers into concise descriptions that can be compared across groups.
In this topic you will calculate averages and spread for both listed data and grouped frequency tables. At Higher tier you will also read medians and quartiles from cumulative frequency diagrams and use interquartile range to compare distributions.
Objectives
- Understand the concept of average
- Calculate the mean, median, mode and range for a discrete data set
- Calculate an estimate for the mean for grouped data
- Identify the modal class for grouped data
- [Higher] Estimate the median from a cumulative frequency diagram
- [Higher] Understand the concept of a measure of spread
- [Higher] Find the interquartile range from a discrete data set
- [Higher] Estimate the interquartile range from a cumulative frequency diagram
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Statistical Measures. 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.
- What is the mean of: 4, 8, 6, 10, 2? A) 5 B) 6 C) 7 D) 8 Answer: B
- The data set 3, 5, 5, 7, 9 has which value as its median? A) 3 B) 5 C) 7 D) 9 Answer: B
- For grouped data, which value is used to estimate the mean? A) The lower class boundary B) The upper class boundary C) The class midpoint D) The class width Answer: C
- The interquartile range measures the spread of which portion of the data? A) The lower 25% B) The upper 25% C) The middle 50% D) The full 100% Answer: C
- If a data set has values 2, 2, 3, 4, 4, 4, 5, what is the mode? A) 2 B) 3 C) 4 D) 5 Answer: C
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Recommended Books
Further learning from open sources
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Textbook section
Measures of the Center of the Data
The "center" of a data set is also a way of describing location. The two most widely used measures of the "center" of the data are the mean (average) and the median . To calculate the mean weight of 50 people, add the 50 weights together and divide by 50. To find the median weight of the 50 people,
"Introductory Statistics: Measures of the Center 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/2-5-measures-of-the-center-of-the-data. Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
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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
Published by other organisations under open licences, credited as they ask. Links open their websites.
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