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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

• 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

• Match graph to data

• Appropriate graph for specific data

• Types

• Bar

• Pareto Charts

• Circle

• Time-series

• Frequency Distributions

• Histograms

• Stem and Leaf Plots

• 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)

• 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.

• “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?

• 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.

• 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.

• Anything that shows the distribution of data into “classes” or intervals.

• Frequency table

• Frequency histogram

• Relative frequency table

• Relative frequency histogram

• 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

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

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

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

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)

• 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