Organizing Data

Displaying data in a chart is a good way of organizing your data, however GRAPHS are invaluable when it comes to organizing your data Displaying data in a chart is a good way of organizing your data, however GRAPHS are invaluable when it comes to organizing your dataWHY????? With graphs you can determine any trend in the data. However it is very Important to use the proper type of graph

Bar Graph Represents 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 When Do I use it? comparing data sets easily Only with discrete data

Broken-Line Graph Broken-Line Graph Involves time-dependent numerical data. Examples of some broken-line graphs are temperature vs day or distance vs time (speed). These plots are 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 or Pie Chart Circle Graph or Pie Chart Displays data as a percentage. Each pie section should have a label and percentage. A total data number should be included. 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

Pictograph Pictograph Uses an icon to represent a quantity of data values in order to decrease the size of the graph. A key or legend must be used to describe 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 Diagram Histogram or Frequency Diagram Histograms displays continuous data in ordered columns. It is a bar graph where bars based on the frequency of the data being measured. Unlike the bar graph there is no separation between the bars and the criteria is now in equal intervals 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 Histogram INTERVALS FREQUENCY 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? Situation Bar Graph or Histogram? We want to compare total revenues of five different companies. We have measured revenues of several companies. We want to compare numbers of companies that make from $0 to $10,000; from $10,000 to $20,000; from $20,000 to $30,000 and so on. We want to compare heights of ten oak trees in a city park. We have measured several trees in a city park. We want to compare numbers of trees that are from 0 to 5 meters high; from 5 to 10; from 10 to 15 and so on. BAR BAR HISTOGRAM HISTOGRAM

Making a Histogram

HISTOGRAMS Step 1 Create a Frequency Table IntervalTallyFrequency [, ) [, )|||| 4 The Intervals are all equal in length

Histograms INTERVALS FREQUENCY The bars show how many times numbers in that interval are found. There are 4 pieces of data in the interval [40, 50) Step 2Create Histogram

Students planning on going to a particular College have submitted their marks 75,78,69,88,89,91,79,74,66,58,82, 70,74,75,70,58,72,82,86,70,76,88, 60,78,77,86,65,74,85,70,76,88,70, 78,76,80,76 Create a Histogram by Hand and summarize the results Example

Relative Frequency You can add another column to your frequency table which shows the frequency of data group as a fraction or percent of the whole data set You can add another column to your frequency table which shows the frequency of data group as a fraction or percent of the whole data set If there is a frequency of 1 out of 30 pieces of data then your relative frequency is If there is a frequency of 1 out of 30 pieces of data then your relative frequency is 0.033

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

Excel Enter Data into your first column Enter Data into your first column Decide on interval Decide on interval Enter Midpoints into second column Enter Midpoints into second column Use Data Analysis Option in the Tools Menu Use Data Analysis Option in the Tools Menu Follow instructions to create Histogram Follow instructions to create Histogram Range is 15 degrees so 2 degree intervals would work. Start at 17.5 and end at 33.5

Fathom *Recommended* on L: drive under Math Department Drop Chart into main page Drop Chart into main page Enter in data Enter in data Drag chart option onto main page Drag chart option onto main page Drag data into chart Drag data into chart Choose Histogram style Choose Histogram style Alter intervals if needed Alter intervals if needed

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