Statistics unit 2 organizing data
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Statistics unit 2 organizing data l.jpg

Statistics Unit 2:Organizing Data

Ms. Hernandez

St. Pius X High School

2006-2007


Saying it with pictures l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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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