Presentation And Analysis
Overview
A specimen Extension paper shows a cumulative frequency graph somebody has drawn from a table of examination marks and asks for two criticisms of it. Not for a calculation, not for a value: for two things the person did wrong. The answers the mark scheme wants are that one cumulative total should be 48 rather than 46, and that the points should be plotted at the ends of the class intervals. That is what this topic is really about: handling data correctly enough that the picture you draw tells the truth.
You will classify data as qualitative, discrete or continuous and as grouped or ungrouped, extract data from printed tables and lists, design and use two-way tables, produce the full range of charts and diagrams from tally charts and pictograms to frequency polygons and histograms with equal class intervals, and calculate the median, mean, range, mode and modal class. On the Extension Tier you add histograms with unequal class intervals, cumulative frequency diagrams, box plots, quartiles, the inter-quartile range and percentiles.
Objectives
- [Core] understand and use qualitative, discrete and continuous data, including grouped and ungrouped data
- [Core] extract data from printed tables and lists
- [Core] design and use two-way tables for grouped and ungrouped data
- [Core] produce charts and diagrams for various data types; scatter graphs, stem-and-leaf, tally charts, pictograms, bar charts, dual and composite bar charts, pie charts, line graphs, frequency polygons, histograms with equal class intervals
- [Extension] histograms with unequal class intervals, cumulative frequency diagrams, box plots
- [Core] calculate median, mean, range, mode and modal class
- [Extension] quartiles and inter-quartile range and percentiles
Mind map
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Presentation And Analysis. Now that you've explored the key concepts and ideas, it's 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.
- Here are seven numbers: 13, 6, 12, 7, 6, 4, 8. What is the range? A. 6 B. 7 C. 8 D. 9 Answer: D
- Which of these is continuous data? A. Shoe size B. Number of goals scored C. The mass of a parcel D. Favourite colour Answer: C
- On a histogram with unequal class intervals, what does the vertical axis show? A. Frequency B. Cumulative frequency C. Frequency density D. Class width Answer: C
- On a cumulative frequency diagram, where should the points be plotted? A. At the midpoint of each class B. At the lower end of each class C. At the upper end of each class D. Anywhere within the class Answer: C
- A class covering 20 < t <= 50 on a histogram has frequency density 1.4. How many values are in the class? A. 1.4 B. 21 C. 30 D. 42 Answer: D
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Recommended Books
Further learning from open sources
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Textbook section
Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
One simple graph, the stem-and-leaf graph or stemplot , comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit . For example, 23 ha
"Introductory Statistics: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar 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/2-1-stem-and-leaf-graphs-stemplots-line-graphs-and-bar-graphs. 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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