Statistical Representation And Measures
Overview
A spreadsheet of 500 numbers tells you nothing at a glance. Turn those same numbers into a chart, or boil them down to a single representative value, and a pattern that was invisible in the raw data suddenly becomes obvious. Choosing the right chart and the right average is what separates a clear report from a confusing one.
This topic covers bar charts, pie charts and histograms with frequency density, then moves to numerical summaries: the mean, median and mode of a discrete data set, an estimate of the mean for grouped frequency data, and how to identify the modal class and the class containing the median when individual values are hidden inside groups.
Objectives
- Use graphical representation of numerical data including bar charts, pie charts and histograms
- Determine the mean, median and mode for a discrete data set
- Calculate an estimate of the mean for grouped frequency data
- Determine a modal class and the class containing the median for grouped data
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Statistical Representation And 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.
- A survey of 40 people found 10 prefer tea. What angle represents 'tea' on a pie chart? A) 45 degrees B) 90 degrees C) 10 degrees D) 250 degrees Answer: B
- A histogram is needed instead of a bar chart when: A) the data is categorical B) the class widths are unequal C) there are more than 5 classes D) the frequencies are all equal Answer: B
- What is the median of: 3, 9, 4, 9, 6, 2? A) 4 B) 5 C) 6 D) 9 Answer: B
- A class 30 <= x < 50 has frequency 40. What is its frequency density? A) 0.5 B) 2 C) 20 D) 1200 Answer: B
- Which statement about the estimated mean of grouped data is correct? A) It is always exactly equal to the true mean B) It uses the class midpoints in place of the real values C) It uses the class upper boundaries in place of the real values D) It cannot be calculated without the raw data Answer: B
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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
Histograms, Frequency Polygons, and Time Series Graphs
For most of the work you do in this book, you will use a histogram to display the data. One advantage of a histogram is that it can readily display large data sets. A rule of thumb is to use a histogram when the data set consists of 100 values or more. A histogram consists of contiguous (adjoining)
"Introductory Statistics: Histograms, Frequency Polygons, and Time Series Graphs" 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/2-2-histograms-frequency-polygons-and-time-series-graphs. 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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