Graphs

There are many different types of graphs, all are used to help show information or data visually. Graphs quickly show changes, compare quantities and in general help prove or disprove a person's point.

Bar Graphs: One of the most widely used graphs, the heights of the bars represent the frequency ( how often something occurs). The graph must include:
  1. Title - should be appropriate to the data, and explain what the graph represents
  2. Horizontal axis (x axis) - must contain a label telling what information is on the axis
  3. Vertical axis (y axis) - must contain a label telling what information is on the axis (generally this axis contains the numerical values)
  4. Interval - this is the numbering on one of the axis (usually the y axis)----- you must choose an appropriate interval, one that will show all of the values ( for example: start with 0 and go to 100)
  5. Scale - this is the value on the interval that each space is, for example-when you number by counting by tens ( 0, 10, 20, 30, .......100)
  6. Key - Double bar graphs (graphs comparing two related quantities ex. Boy vs girl) must contain a key, to let you know what each color bar represents

Here's an example of a bar graph:

  1. Title: What is your favorite sport?
  2. Horizontal Axis Label: types of sports, each bar is also labeled with the specific type of sport
  3. Vertical Axis Label: # of students
  4. Interval: 0-10, since no one voted more than 10
  5. Scale: counting by one's, since there is not a lot of numbers
  6. Key: dark blue is for boys, light blue is for girls
Line Graphs: line graphs are used to show changes over time, the upwardness of a line easily shows an increasing trend, a downwardness of a line generally shows a decreasing trend. If a line remains horizontal, then there was no change, it remained constant.

The graph must include:

Pie Charts / Circle graphs: This chart uses percents to compare area that each sector or slice of the circle has. For example The amount of money you spend on things during the year.

To make it easy lets assume your total Budget is $100.
Expense Amount out of total Percent
food 20/100 20%
clothing 50/100 50%
music 15/100 15%
movies 15/100 15%

Then, change each percent to a piece of the 360 degree circle. Do this by multiplying the decimal form of the percent by 360.
Percent Work Degree
20% .20 x 360 72
50% .50 x 360 180
15% .15 x 360 54
15 % .15 x 360 54

Then use a protractor to divide the circle into the correct degree sectors. Color each sector and label each sector with the PERCENT and Title in which the sector is representing. Don't Forget to give the Graph a TITLE!!!!!



Line Plots: Line plots are similar to bar graphs, but the use X's (pilled on top of each other) to represent the frequency. There is only a horizontal axis, which is labeled, and a title. The X's should be the same size so you can compare the heights.

Stem & Leaf Diagrams: Stem and leaf diagrams use the same concept as bar graphs (length is used to compare) yet also show the exact data, which bar graphs do not! You get the best of both worlds !!!!!!

The Stem and Leaf Diagram break the numbers (generally) in to tens and ones digits. For example the number 28 would be broken into 2 (for the Stem: tens digit) and 8 (for the Leaf: ones digit) The Stems are ordered least to greatest and so are each of the leaves.

Here's the data: 10, 12, 14, 15, 15, 28, 30, 30, 31, 49, 49, 50, 55, 56, 60, 69, 100,102

Stem Leaf
1 0 2 4 5 5 5
2 8
3 0 0 1
4 9 9
5 0 5 6
6 0 9
7
8
9
10 0 2

Notice how nothing occurs in the 70's, 80's, or 90's. Notice that 15 is the mode because it appears the most (three 5's in a row). Notice that the 10's interval occurs the most (it is the longest string of numbers). Also look and see that the 30's and 60's intervals occur the same number of times. 100 and 102 are outliers (numbers that are separate from most of the data.)

Frequency Charts: Are charts that help organize data before you make your graphs. The chart has a title and usually three columns like below:

Favorite Ice Cream

Flavor Tally Frequency
chocolate IIII 4
vanilla III 3
strawberry 0
Choc. Chip II 2

If you total the frequency column you should get the total number of people that answered the question. The Frequency tells you how tall to make the bar in a bar graph, or how many X's to pile on top of each other in a line plot.

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