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Introduction to Statistics: Data Organization and Analysis

Learn the basics of statistics, including collecting, organizing, summarizing, and analyzing data to draw conclusions or answer questions. Understand qualitative and quantitative variables, and how to organize and summarize data using frequency distributions and graphical representations.

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Introduction to Statistics: Data Organization and Analysis

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  1. Chapter 1Section 1 Introduction to the Practice of Statistics

  2. Chapter 1 – Section 1 • The science of statistics is • Collecting • Organizing • Summarizing • Analyzing information to draw conclusions or answer questions

  3. Chapter 1 – Section 1 • Organize and summarize the information Descriptive statistics (chapters 2 through 4) • Draw conclusion/generalization from the information Inferential statistics (chapters 9 through 11)

  4. Chapter 1 – Section 1 • A population - Is the group to be studied - Includes all of the individuals in the group • A sample • Is a subset of the population • Is often used in analyses because getting access to the entire population is impractical

  5. Chapter 1 – Section 1 • Characteristics of the individuals under study are called variables • Some variables have values that are attributes or characteristics … those are called qualitative or categorical variables • Some variables have values that are numeric measurements … those are called quantitative variables • The suggested approaches to analyzing problems vary by the type of variable

  6. Chapter 1 – Section 1 • Examples of qualitative variables • Gender • Zip code • Blood type • States in the United States • Brands of televisions • Qualitative variables have category values … those values cannot be added, subtracted, etc.

  7. Chapter 1 – Section 1 • Examples of quantitative variables • Temperature • Height and weight • Sales of a product • Number of children in a family • Points achieved playing a video game • Quantitative variables have numeric values … those values can be added, subtracted, etc.

  8. Chapter 1 – Section 1 • Quantitative variables can be either discrete or continuous • Discrete variables • Variables that have a finite or a countable number of possibilities • Frequently variables that are counts • Continuous variables • Variables that have an infinite but not countable number of possibilities • Frequently variables that are measurements

  9. Chapter 1 – Section 1 • Examples of discrete variables • The number of heads obtained in 5 coin flips • The number of cars arriving at a McDonald’s between 12:00 and 1:00 • The number of students in class • The number of points scored in a football game • The possible values of qualitative variables can be listed

  10. Chapter 1 – Section 1 • Examples of continuous variables • The distance that a particular model car can drive on a full tank of gas • Heights of college students

  11. Summary: Chapter 1 – Section 1 • The process of statistics is designed to collect and analyze data to reach conclusions • Variables can be classified by their type of data • Qualitative or categorical variables • Discrete quantitative variables • Continuous quantitative variables

  12. Chapter 2 Organizing and Summarizing Data

  13. Chapter 2 Sections • Sections in Chapter 2 • Organizing Qualitative Data • Organizing Quantitative Data • Graphical Misrepresentations of Data

  14. Chapter 2Section 1 Organizing Qualitative Data

  15. Chapter 2 – Section 1 • Qualitative data values can be organized by a frequencydistribution • A frequency distribution lists • Each of the categories • The frequency for each category

  16. Chapter 2 – Section 1 • A simple data set is blue, blue, green, red, red, blue, red, blue • A frequency table for this qualitative data is • The most commonly occurring color is blue

  17. Chapter 2 – Section 1 • The relativefrequencies are the proportions (or percents) of the observations out of the total • A relative frequency distribution lists • Each of the categories • The relative frequency for each category

  18. Chapter 2 – Section 1 • A relative frequency table for this qualitative data is • A relative frequency table can also be constructed with percents (50%, 12.5%, and 37.5% for the above table)

  19. Chapter 2 – Section 1 • Bar graphs for our simple data (using Excel) • Frequency bar graph • Relative frequency bar graph

  20. Chapter 2 – Section 1 • A Paretochart is a particular type of bar graph • A Pareto differs from a bar chart only in that the categories are arranged in order • The category with the highest frequency is placed first (on the extreme left) • The second highest category is placed second • Etc. • Pareto charts are often used when there are many categories but only the top few are of interest

  21. Chapter 2 – Section 1 • A Pareto chart for our simple data (using Excel)

  22. Chapter 2 – Section 1 • An example side-by-side bar graph comparing educational attainment in 1990 versus 2003

  23. Chapter 2 – Section 1 • An example of a pie chart

  24. Chapter 2Section 2 Organizing Quantitative Data:

  25. Chapter 2 – Section 2 • Consider the following data • We would like to compute the frequencies and the relative frequencies

  26. Chapter 2 – Section 2 • The resulting frequencies and the relative frequencies

  27. Chapter 2 – Section 2 • Example of histograms for discrete data • Frequencies • Relative frequencies

  28. Chapter 2 – Section 2 • Continuous data cannot be put directly into frequency tables since they do not have any obvious categories • Categories are created using classes, or intervals of numbers • The continuous data is then put into the classes

  29. Chapter 2 – Section 2 • For ages of adults, a possible set of classes is 20 – 29 30 – 39 40 – 49 50 – 59 60 and older • For the class 30 – 39 • 30 is the lowerclasslimit • 39 is the upperclasslimit • The classwidth is the difference between the upper class limit and the lower class limit • For the class 30 – 39, the class width is 40 – 30 = 10

  30. Chapter 2 – Section 2 • All the classes have the same widths, except for the last class • The class “60 and above” is an open-endedclass because it has no upper limit • Classes with no lower limits are also called open-ended classes

  31. Chapter 2 – Section 2 • The classes and the number of values in each can be put into a frequency table • In this table, there are 1147 subjects between 30 and 39 years old

  32. Chapter 2 – Section 2 • Good practices for constructing tables for continuous variables • The classes should not overlap • The classes should not have any gaps between them • The classes should have the same width (except for possible open-ended classes at the extreme low or extreme high ends) • The class boundaries should be “reasonable” numbers • The class width should be a “reasonable” number

  33. Chapter 2 – Section 2 • Just as for discrete data, a histogram can be created from the frequency table • Instead of individual data values, the categories are the classes – the intervals of data

  34. Chapter 2 – Section 2 • A stem-and-leafplot is a different way to represent data that is similar to a histogram • To draw a stem-and-leaf plot, each data value must be broken up into two components • The stem consists of all the digits except for the right most one • The leaf consists of the right most digit • For the number 173, for example, the stem would be “17” and the leaf would be “3”

  35. Chapter 2 – Section 2 • In the stem-and-leaf plot below • The smallest value is 56 • The largest value is 180 • The second largest value is 178

  36. Chapter 2 – Section 2 • To draw a stem-and-leaf plot • Write all the values in ascending order • Find the stems and write them vertically in ascending order • For each data value, write its leaf in the row next to its stem • The resulting leaves will also be in ascending order • The list of stems with their corresponding leaves is the stem-and-leaf plot

  37. Chapter 2 – Section 2 • Modifications to stem-and-leaf plots • Sometimes there are too many values with the same stem … we would need to split the stems (such as having 10-14 in one stem and 15-19 in another) • If we wanted to compare two sets of data, we could draw two stem-and-leaf plots using the same stem, with leaves going left (for one set of data) and right (for the other set)

  38. Chapter 2 – Section 2 • A dotplot is a graph where a dot is placed over the observation each time it is observed • The following is an example of a dot plot

  39. Chapter 2 – Section 2 • A useful way to describe a variable is by the shape of its distribution • Some common distribution shapes are • Uniform • Bell-shaped (or normal) • Skewed right • Skewed left

  40. Chapter 2 – Section 2 • A variable has a uniform distribution when • Each of the values tends to occur with the same frequency • The histogram looks flat

  41. Chapter 2 – Section 2 • A variable has a bell-shaped distribution when • Most of the values fall in the middle • The frequencies tail off to the left and to the right • It is symmetric

  42. Chapter 2 – Section 2 • A variable has a skewedright distribution when • The distribution is not symmetric • The tail to the right is longer than the tail to the left • The arrow from the middle to the long tail points right Right

  43. Chapter 2 – Section 2 • A variable has a skewedleft distribution when • The distribution is not symmetric • The tail to the left is longer than the tail to the right • The arrow from the middle to the long tail points left Left

  44. Summary: Chapter 2 – Section 2 • Quantitative data can be organized in several ways • Histograms based on data values are good for discrete data • Histograms based on classes (intervals) are good for continuous data • The shape of a distribution describes a variable … histograms are useful for identifying the shapes

  45. Chapter 2Section 3 Graphical Misrepresentations of Data

  46. Chapter 2 – Section 4 • The two graphs show the same data … the difference seems larger for the graph on the left • The vertical scale is truncated on the left

  47. Chapter 2 – Section 4 • The gazebo on the right is twice as large in each dimension as the one on the left • However, it is much more than twice as large as the one on the left Original “Twice” as large

  48. Summary: Chapter 2 – Section 1 • Qualitative data can be organized in several ways • Tables are useful for listing the data, its frequencies, and its relative frequencies • Charts such as bar graphs, Pareto charts, and pie charts are useful visual methods for organizing data • Side-by-side bar graphs are useful for comparing two sets of qualitative data

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