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Presentation Transcript

Saying it with Pictures

- Organizing Data
- Graphic Summaries
- Show data
- Encourage reader focus on data
- Yet, avoid distorting what data have to say
- See examples on pg 40 compare/contrast

Basic Graphs

- Match graph to data
- Appropriate graph for specific data

- Types
- Bar
- Pareto Charts
- Circle
- Time-series
- Frequency Distributions
- Histograms
- Stem and Leaf Plots

Bar Graphs

- Bars are vertical or horizontal
- Bars are uniform and evenly spaced
- Length of bar represents the value of the variable that is being displayed
- Percentage or frequency

- Same measurement scale is use for each bar
- Title, labels (bar, axis, value)

Examples

- Page 42, 43 (good ex)
- Page 90 (bad ex)
- Compare/contrast the “good” vs “bad” examples of bar graphs on pages 42, 43, and 90.
- What kind of data is appropriate for a bar graph?

Quantitative or Qualitative data

Quantitative Data: Measurement itself is usually displayed. Measurement scale should be consistent.

Qualitative Data: Frequency or percentage of occurrence is usually displayed.

Pareto Charts

- “Pa-ray-toe” Charts
- Specific type of bar graph
- Bar height represents frequency of event
- Bar are arranged from left to right – decreasing height
- Example on page 44
What kind of data is appropriate for a Pareto Chart?

Identify the frequency of events or categories in decreasing order of frequency of occurrence

Say what?

Circle Graphs

- AKA “pie” chart
- Percentages
- Examples on pg 45, 98
- What kind of data is appropriate for a circle graph?

Display how a TOTAL is dispersed into several categories. Mostly for Qualitative data, or anything where the percentage of occurrence makes sense.

10 or less categories is best.

Time-Series Graph

- Data are plotted in order of occurrence at regular intervals over a period of time
- Measure same thing over a period of time at specific (hopefully) periods of time
- Distance jogged in 30 minutes (pg 47)
- Stock price for Coca-Cola (pg 52)
- Stock price history for Mickey D’s (pg 52)
What kind of data is appropriate for a time-series graph?

Display how data change over a period of time.

Keep consistent units of time.

Frequency Distributions

- Anything that shows the distribution of data into “classes” or intervals.
- Frequency table
- Frequency histogram
- Relative frequency table
- Relative frequency histogram

Classes or Intervals

- First need a frequency table (pg 53)
- The frequency table organizes data
- In the frequency table WE make distinct data intervals that cover all the data
- These intervals are called “classes”
- The classes are disjoint
- Each data value will fall in one and only one interval or class
- Corresponds to one bar in a histogram

Example 3 on pages 53-56From a Frequency Table to a Histogram

- List all data recorded
- Make a Frequency Table:
- Think about how many classes you will use
- Too few and you will lose the variability in the data (only see the tree in the forest)
- Too many and you many not really see a summary (see all trees in the forest but not the forest)

- Next, determine the CLASS WIDTH
- Page 54

- Next, determine the CLASS RANGE (aka Class Limits)
- Page 54

- Next, calculate the CLASS MIDPOINT
- Page 55

- Finally, you are now ready to construct your histogram

Example 3 on pages 53-56From a Frequency Table to a Histogram

- 6 classes (we already determined this … well its from ex 3)
- Next, determine the CLASS WIDTH (pg 54)
- Largest data value minus the smallest data value divided by the numer of class you decided to use
- Round up to the nearest whole number
- 7.7 is rounded up to 8
- So now we have 6 classes and with width of 8
- The widths correspond to data values
- Data values from 1-8, 9-16, 17-24, 25-32, 33-40, 41-48 (bottom of pg 54)

- Next, determine the CLASS RANGE (aka Class Limits)
- Page 54

- Next, calculate the CLASS MIDPOINT
- Page 55

- Finally, you are now ready to construct your histogram

Example 3 on pages 53-56From a Frequency Table to a Histogram

- 6 CLASSES
- CLASS WIDTH is 8
- Next, determine the CLASS RANGE (aka Class Limits , pg 54)
- Limits are the smallest (lower limit) and the largest (upper limit) data value that can be in any one class
- In the first class, the width is 1 to 8
- lowest value is 0.5 (less than 1) and the highest value is (8.5)

- In the second class, the width is 9-16
- lowest value is 8.5 (less than 1) and the highest value is (16.5)

- And so on … see bottom of page 54

- Next, calculate the CLASS MIDPOINT
- Page 55

- Finally, you are now ready to construct your histogram

Example 3 on pages 53-56From a Frequency Table to a Histogram

- 6 CLASSES
- CLASS WIDTH is 8
- CLASS RANGE (aka Class Limits , pg 54)
- Next, calculate the CLASS MIDPOINT (pg 55)
- Midpoint is usually used to represent the data in each class
- It’s the “class representative”
- Lower limit minus the upper limit and divide by two
- Calculated for each class

- Finally, you are now ready to construct your histogram

Example 3 on pages 53-56From a Frequency Table to a Histogram

- 6 CLASSES
- CLASS WIDTH is 8
- CLASS RANGE (aka Class Limits , pg 54)
- CLASS MIDPOINT (pg 55)
- Finally, you are now ready to construct your histogram
- But wait! We need CLASS BOUNDARIES!!!
- The bars touch in a histogram
- Upper class boundary
- Add 0.5 unit to upper class limit

- Lower class boundary
- Add 0.5 unit to lower class limit

Example 3 on pages 53-56From a Frequency Table to a Histogram

- Make a Frequency Table
- Example is on page 54
- Procedure is summarized on page 56

- 6 CLASSES
- CLASS WIDTH is 8
- CLASS RANGE (aka Class Limits , pg 54)
- CLASS MIDPOINT (pg 55)
- CLASS BOUNDARIES (pg 55-56)
- Draw Histogram (pg 56)
- Procedure is summarized on page 56

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