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statistics unit 2 organizing data

Statistics Unit 2:Organizing Data

Ms. Hernandez

St. Pius X High School

2006-2007

saying it with pictures
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
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
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
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
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
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
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
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
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 56 from a frequency table to 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 56 from a frequency table to a histogram12
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 56 from a frequency table to a histogram13
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 56 from a frequency table to a histogram14
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 56 from a frequency table to a histogram15
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 56 from a frequency table to a histogram16
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