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# eqw - PowerPoint PPT Presentation

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### Statistics Unit 2:Organizing Data

Ms. Hernandez

St. Pius X High School

2006-2007

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)
• 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
• 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
• 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
• 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
• 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
• 6 CLASSES
• CLASS WIDTH is 8
• CLASS RANGE (aka Class Limits , pg 54)
• CLASS MIDPOINT (pg 55)
• 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
• 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