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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

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

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

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 53-56 From 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

Next, determine the CLASS RANGE (aka Class Limits)

Next, calculate the CLASS MIDPOINT

Finally, you are now ready to construct your histogram

Example 3 on pages 53-56 From 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)

Next, calculate the CLASS MIDPOINT

Finally, you are now ready to construct your histogram

Example 3 on pages 53-56 From 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

Finally, you are now ready to construct your histogram

Example 3 on pages 53-56 From 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 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 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