Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 1 of 27 Chapter 2 Section 1 Organizing Qualitative Data

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 2 of 27 Chapter 2 – Section 1 ●Learning objectives  Organize qualitative data in tables  Construct bar graphs  Construct pie charts 1 2 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 3 of 27 Chapter 2 – Section 1 ●Learning objectives  Organize qualitative data in tables  Construct bar graphs  Construct pie charts 1 2 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 4 of 27 Chapter 2 – Section 1 ●Raw qualitative data comes as a list of values … each value is one out of a set of categories ●These values can be organized as either a long list or in a table ●Raw qualitative data comes as a list of values … each value is one out of a set of categories ●These values can be organized as either a long list or in a table ●Interpreting the list of data can be difficult, particularly if there is a lot of data ●Methods are needed to aid interpretation

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 5 of 27 Chapter 2 – Section 1 ●Qualitative data values can be organized by a frequency distribution ●A frequency distribution lists  Each of the categories  The frequency for each category

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 6 of 27 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 ColorFrequency Blue4 Green1 Red3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 7 of 27 Chapter 2 – Section 1 ●The frequencies are the counts of the observations ●The relative frequencies are the proportions (or percents) of the observations out of the total ●The frequencies are the counts of the observations ●The relative frequencies 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

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 8 of 27 Chapter 2 – Section 1 ●Use the same simple set of data blue, blue, green, red, red, green, blue, blue ●A relative frequency table is computed as follows  Sum of all frequencies = 8 (there are 8 observations)  Blue has a relative frequency of 4 / 8 =.500  Green has a relative frequency of 1 / 8 =.125  Red has a relative frequency of 3 / 8 =.375

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 9 of 27 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) ColorRelative Frequency Blue.500 Green.125 Red.375

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 10 of 27 Chapter 2 – Section 1 ●Tables are useful because they provide an exact count for the data ●However, if the data set is medium to large in size, it may be difficult to understand the data when presented in a table ●Additional techniques are needed to give a better idea of “the big picture”

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 11 of 27 Chapter 2 – Section 1 ●Learning objectives  Organize qualitative data in tables  Construct bar graphs  Construct pie charts 1 2 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 12 of 27 Chapter 2 – Section 1 ●In general, pictures of data send a more powerful message than tables ●Visual methods, such as bar graphs, present a better summary than just a table ●In general, pictures of data send a more powerful message than tables ●Visual methods, such as bar graphs, present a better summary than just a table ●A bar graph  Lists the categories on the horizontal axis  Draws rectangles above each category where the heights are equal to the category’s frequency or relative frequency

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 13 of 27 Chapter 2 – Section 1 ●Bar graphs for our simple data (using Excel)  Frequency bar graph  Relative frequency bar graph

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 14 of 27 Chapter 2 – Section 1 ●Good practices in constructing bar graphs ●The horizontal scale  The categories should be spaced equally apart  The rectangles should have the same widths ●Good practices in constructing bar graphs ●The horizontal scale  The categories should be spaced equally apart  The rectangles should have the same widths ●The vertical scale  Should begin with 0  Should be incremented in reasonable steps  Should go somewhat, but not significantly, beyond the largest frequency or relative frequency

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 15 of 27 Chapter 2 – Section 1 ●A Pareto chart 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. ●A Pareto chart 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

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 16 of 27 Chapter 2 – Section 1 ●A Pareto chart for our simple data (using Excel)

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 17 of 27 Chapter 2 – Section 1 ●An example with more data values ●A data set from the text ●Even with only 30 data values, this table cannot be interpreted easily

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 18 of 27 Chapter 2 – Section 1 ●Graphs for this set of data  A frequency bar graph  A relative frequency bar graph ●These graphs are more effective than the table

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 19 of 27 Chapter 2 – Section 1 ●Graphs for this data (continued)  A Pareto chart

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 20 of 27 Chapter 2 – Section 1 ●Two qualitative variables can be compared by comparing their bar graphs ●A side-by-side bar graph draws two rectangles for each category, one for each variable ●The frequencies (or relative frequencies) for each category can be compared

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 21 of 27 Chapter 2 – Section 1 ●An example side-by-side bar graph comparing educational attainment in 1990 versus 2003

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 22 of 27 Chapter 2 – Section 1 ●Learning objectives  Organize qualitative data in tables  Construct bar graphs  Construct pie charts 1 2 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 23 of 27 Chapter 2 – Section 1 ●A pie chart is a circle divided into sections, one for each category ●The area (angle) of each sector is proportional to the frequency of that category ●Pie charts are useful to show the relative proportions of each category, compared to the whole

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 24 of 27 Chapter 2 – Section 1 ●Good practices for constructing pie charts  Different colors should be used to distinguish the categories  Each category should be labeled with the category name and relative frequency ●Good practices for constructing pie charts  Different colors should be used to distinguish the categories  Each category should be labeled with the category name and relative frequency ●Pie charts are not as effective if there are too many categories or if some relative frequencies are too small

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 25 of 27 Chapter 2 – Section 1 ●An example of a pie chart for the 2003 data from the side-to-side bar chart

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 26 of 27 Chapter 2 – Section 1 ●Side-by-side pie charts are used sometimes, but can be difficult to interpret (using Excel, with substantial modifications)

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 2 Section 1 – Slide 27 of 27 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