1. Graphs Another good way to organize this data is with a Graph. Graph – a diagram that shows a relationship between two sets of numbers. So do we have two sets of numbers? Yes. Can I make a diagram from these two sets of numbers? Yes

2. Graphs Each point on the graph is called a data point and can be described with an x value (year) and y value (time). So to find the fastest time for a given year, trace to that year on the x-axis then trace up to the data point. The height of the point on the y-axis is the value of the time for that year.

3. Circle Graph - graph in the form of a circle that is divided into sectors, with each sector representing a part of a set of data. This sector is being compared to the whole. 42%+25%+33%=100% Circle Graphs

4. Making Circle Graphs 1. Find the percentage that each value represents. Purple 35/100 = 35% Green 10/100 = 10% Red 7/100 = 7% Yellow 3/100 = 3% Dark Blue 20/100 = 20% Light Blue 25/100 = 25%

5. Making Circle Graphs Divide the circle into each section using the number of degrees. Label each section with the percentage and its title. Purple Green Red Yellow Dark Blue Light Blue

6. Line Graph Line Graph - A type of graph that shows trends by drawing connecting lines between data points. For this type of graph, we connect each data point with straight lines. That is where this type of graph gets its name. These lines help us to see how the values are changing over each year.

7. Bar Graph Bar Graph – a type of graph in which the y value (vertical value) is represented with a bar to that value. Ex.

8. Histogram Histogram – a type of bar graph in which the bars represent equally spaced intervals of time. Ex.

9. Pictographs Pictograph - a method of representing statistical data using symbolic figures to match the frequencies of different kinds of data. Example: The pictograph shows the number of varieties of apples stored at a supermarket.

10. Making a Pictograph To Create a Pictograph: 1.Determine which figure you will use to represent the data. 2.Determine the value that the figure will hold. ( ex. A picture of a car represents 1,000 cars.) 3.Create a graph (either vertical or horizontal) using the figure to represent the quantities.

11. Time Lines Time Line – a graph that shows the dates of several historical events. The graph is usually represented using a single horizontal axis.

12. Making a Time Line To Create a Time Line: 1.List all events in chronological order. 2.Find the range of the dates. 3.Find an appropriate interval for the dates. 4.Create a horizontal axis and draw tick marks to label the minimum, maximum, and intervals. 5.Put the events onto the graph at the appropriate year.

13. Frequency Distribution Frequency Distribution – a table showing the the number of events or items in consecutive intervals. Example – Grades on a Test. 10 students took a test and scored as follows: 67, 72, 85, 89, 90, 91, 92, 93, 95,100

14. Frequency Distribution 1.Find the intervals for the grades. 60-69,70-79,80-89,90-99,100-109 2.Create a table showing the interval, tally, and total for each interval.

15. Frequency Distribution 1.Find the intervals for the grades. 60-69,70-79,80-89,90-99,100-109 2.Create a table showing the interval, tally, and total for each interval.

16. Line Plots Characteristics of Line plots: 1.Line plots use one axis or Line to graph data. 2.On this line, we place the appropriate scale and interval for our data. 3.Line plots use x’s above a value to show an occurance of that value. (example: if I have four 3’s, I would put four x’s above 3 on my line plot.

17. Line Plot - Example Suppose thirty people live in an apartment building. These are the following ages: 58, 30, 37, 36, 34, 49, 35, 40, 47, 47, 39, 54, 47, 48, 54, 50, 35, 40, 38, 47, 48, 34, 40, 46, 49, 47, 35, 48, 47, 46 Step 1 Your first step should be: placing the values in ascending numerical order. 30, 34, 34, 35, 35, 35, 36, 37, 38, 39, 40, 40, 40, 46, 46, 47, 47, 47, 47, 47, 47, 48, 48, 48, 49, 49, 50, 54, 54, 58

18. Step 2 Draw a line with a ruler and divide it into equal segments. The number of segments depends on your data set. Find the smallest and largest values and determine a suitable scale. The line should be at least.5 of a page width. Step 3 Put an X above the line at an appropriate place. Continue until all of the data points are plotted. Line Plot - Example (Continued)

19. Scatter Plot Scatter plot – a type of graph that shows the relationship between two sets of data. In this type of graph, single points are used to represent relationships between the two sets of data.

20. Scatter Plot Positive Correlation- the y- coordinates tend to increase as the x-coordinates increase. Negative Correlation- the y- coordinates tend to decrease as the x-coordinates increase. No Correlation – no pattern exists between the coordinates.

21. Choosing the Appropriate Graph Use a bar graph when the data fall into distinct categories and you want to compare totals. Use a line graph when the categories have a numerical order, such as a sequence of years. Use a pictograph instead of a bar graph when you want high visual appeal.

22. Why are Graphs Misleading? Most of the time, it has to do with the scale. –Either the scale on the x-axis or –The scale on the y-axis

23. Misleading Graphs - Example To show this, I would like to do two examples. The sales for a certain company over the past 15 years. Suppose I say that the sales for this company for the past years are as follows.

24. (Y-axis) Scale of 0 - 2,500,000 Each year seems to have the same height, or at least close to it. How can I better show the difference in the height of each bar? Misleading Graphs – Example (Continued)

25. (Y-axis) Scale of 1,900,000 - 2,500,000 When I make the scale smaller, I can better see the difference in the height of each of the bars. This shows me that the sales have gone up for the past 4 years. If I had used a larger scale, I would not be able to see this as easily. Misleading Graphs – Example (Continued)