Organizing Organizing DataData

Displaying data in a chart is a good way of Displaying data in a chart is a good way of organizing your data, however GRAPHS organizing your data, however GRAPHS are invaluable when it comes to organizing are invaluable when it comes to organizing your datayour data

WHY?????WHY?????

With graphs you can determine any trend With graphs you can determine any trend in the data. in the data.

However it is very Important to use the However it is very Important to use the proper type of graphproper type of graph

Bar GraphRepresents discrete data (counted or categorical). The vertical bars are equally set apart and are used to display quantities.

A double bar graph can be used to compare two sets.

Data categories are Nominal typically

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Distance (km)

Mo

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Tu

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da

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Th

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da

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Fri

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turd

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Day of the Week

Distance Travelled on Our Vacation

When Do I use it?

• comparing data sets easily

•Only with discrete data

Patient's Mass

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76

76.5

77

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Broken-Line GraphBroken-Line GraphInvolves time-dependent numerical Involves time-dependent numerical data. Examples of some broken-line data. Examples of some broken-line graphs are temperature vs day or graphs are temperature vs day or distance vs time (speed). These plots distance vs time (speed). These plots are useful for indicating trendsare useful for indicating trends. .

When Do I Use It?

•To show values between known data. Simple and easy to visualize

•Makes many assumptions

Circle Graph Circle Graph or Pie Chartor Pie Chart

Displays data as a Displays data as a percentage. Each percentage. Each pie section should pie section should have a label and have a label and percentage. A total percentage. A total data number should data number should be includedbe included..

Countries Visited

Belgium 5%

Portugal 10%

Spain 20%

France 40%

England 25%

When Do I Use It?

•Harder to compare between sets but good to demonstrate data compared to overall.

•No exact numerical data is given

•Best with 3-7 categories

•Used only with discrete data

PictographPictographUses an icon to represent a quantity of Uses an icon to represent a quantity of data values in order to decrease the data values in order to decrease the size of the graph.size of the graph.

A key or legend must be used to A key or legend must be used to describe the icondescribe the icon

When Do I Use It?

•Visually Appealing

•Handles large data sets easily

•Hard to quantify partial icons

•Best for small amount of categories

•Very simplistic

Histogram or Frequency Histogram or Frequency DiagramDiagram

Histograms displays continuous data in ordered Histograms displays continuous data in ordered columns. It is a bar graph where bars based on columns. It is a bar graph where bars based on the the frequencyfrequency of the data being measured. of the data being measured.

Unlike the bar graph there is no separation Unlike the bar graph there is no separation between the bars and the criteria is now in between the bars and the criteria is now in equal intervalsequal intervals of measurement of measurement

When Do I use it?

•Used to make comparisons, particularly against the “bell” curve

•Only use with Continuous data

•Limited to one data set

•Visually Appealing

A HistogramA Histogram

INTERVALS

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40 50 60 70 80 90 100

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The bars show how many times numbers in that interval are found.

There are 4 pieces of data in the interval [40, 50)

What Graph to Use?What Graph to Use?SituationSituation Bar Graph or Histogram?Bar Graph or Histogram?

We want to compare total revenues We want to compare total revenues of five different companies.of five different companies.

We have measured revenues of We have measured revenues of several companies. We want to several companies. We want to compare numbers of companies compare numbers of companies that make from $0 to $10,000; that make from $0 to $10,000; from $10,000 to $20,000; from from $10,000 to $20,000; from $20,000 to $30,000 and so on.$20,000 to $30,000 and so on.

We want to compare heights of ten We want to compare heights of ten oak trees in a city park.oak trees in a city park.

We have measured several trees in We have measured several trees in a city park. We want to compare a city park. We want to compare numbers of trees that are from 0 numbers of trees that are from 0 to 5 meters high; from 5 to 10; to 5 meters high; from 5 to 10; from 10 to 15 and so on.from 10 to 15 and so on.

BARBAR

BARBAR

HISTOGRAMHISTOGRAM

HISTOGRAMHISTOGRAM

Making a HistogramMaking a Histogram

HISTOGRAMSHISTOGRAMS

Step 1 Step 1 Create a Frequency TableCreate a Frequency Table

IntervalInterval TallyTally FrequencyFrequency

[ , ) [ , ) |||||||| 44

[ , )[ , )

The Intervals are all equal in length

HistogramsHistograms

INTERVALS

FR

EQ

UE

NC

Y

40 50 60 70 80 90 100

8

6

4

2

0

The bars show how many times numbers in that interval are found.

There are 4 pieces of data in the interval [40, 50)

Step 2 Create Histogram

Students planning on going to a particular Students planning on going to a particular College have submitted their marksCollege have submitted their marks

75,78,69,88,89,91,79,74,66,58,82, 75,78,69,88,89,91,79,74,66,58,82, 70,74,75,70,58,72,82,86,70,76,88, 70,74,75,70,58,72,82,86,70,76,88, 60,78,77,86,65,74,85,70,76,88,70, 60,78,77,86,65,74,85,70,76,88,70, 78,76,80,7678,76,80,76

Create a Histogram by Hand and Create a Histogram by Hand and summarize the resultssummarize the results

ExampleExample

Relative FrequencyRelative Frequency

You can add another column to your You can add another column to your frequency table which shows the frequency table which shows the frequency of data group as a fraction frequency of data group as a fraction or percent of the whole data setor percent of the whole data set

If there is a frequency of 1 out of 30 If there is a frequency of 1 out of 30 pieces of data then your relative pieces of data then your relative frequency is 0.033frequency is 0.033

You can graph this on your histogram You can graph this on your histogram as a broken line graphas a broken line graph

ExcelExcel Enter Data into your first columnEnter Data into your first column Decide on intervalDecide on interval Enter Midpoints into second columnEnter Midpoints into second column Use Data Analysis Option in the Tools Use Data Analysis Option in the Tools

MenuMenu Follow instructions to create Follow instructions to create

HistogramHistogram

Range is 15 degrees so 2 degree intervals would work. Start at 17.5 and end at 33.5

Fathom *Recommended*Fathom *Recommended*on L: drive under Math Departmenton L: drive under Math Department

Drop Chart into main pageDrop Chart into main page Enter in dataEnter in data Drag chart option onto main pageDrag chart option onto main page Drag data into chartDrag data into chart Choose Histogram styleChoose Histogram style Alter intervals if neededAlter intervals if needed

HomeworkHomework

Pg 101 #1, 2, 5, 8 use fathom to Pg 101 #1, 2, 5, 8 use fathom to create a histogram, 15create a histogram, 15