GraphsGraphsDisplaying Data

GraphingGraphing Graphs are visual displays of data. Different types of graphs are used for

different purposes. The correct type of graph must be used for

the data collected. In other words, the data determines the graph

type…you don’t choose the type you want!

Discrete or Continuous?Discrete or Continuous? When deciding on the type of graph to make, ask

yourself: Is my independent variable discrete or continuous?

Discrete variables are categorical e.g.: gender, brand of fertilizer, type of sandwich Use a BAR GRAPH with these variables

Continuous variables are associated with measurements involving a standard scale with equal intervals e.g. amount of fertilizer in grams, time in seconds Use a LINE GRAPH with these variables

Graph TypesGraph Types Line graph

Shows relationship between two variables Used to help show the trend, or pattern, in data Trends allow for predictions Independent variable goes on horizontal axis (x) Dependent variable goes on vertical axis (y)

Bar graphs Display data that is not continuous Used to show comparisons between different sets of data or

categories Pie Chart

Uses circle sections to show parts of a whole

Making a Line GraphMaking a Line Graph Will be used in most of our experiments Must have title, labeled axes, & units Must have reasonable spacing Line must take up graph space

Line shouldn’t be to right or left of graph space Line shouldn’t be to top or bottom of graph space Line should be fairly centered, so make axis numbers fit your

data Line should extend through (0,0) point when appropriate Line should NOT extend through (0,0) point when NOT

appropriate

Line Graph ExampleLine Graph Example What is this a graph

of?

How do you know?

N.Y. Temperatures

Title

Line Graph from DataLine Graph from Data

Time is continuous. There are other time measurements possible between the measurements recorded. The experimenter could have recorded the temperature every hour, every half hour, or every minute. Therefore, a line graph is appropriate.

Best-Fit Line Graph best fit line graph

– see p. 18 Connects with

best smooth & continuous line

Doesn’t necessarily go through all data points

gets average.

Best-Fit Line GraphAll show trend All allow for prediction

Straight-line fit Smooth curve fit Smooth curve fit

Bar GraphBar Graph

A Bar Graph is appropriate here because the data shows lunch choices. Each choice is a separate category

Bar GraphBar Graph

Categories are the horizontal axis.

Measurements are on the vertical axis.

Each category has a separate bar.

Pie Chart Pie Chart (Circle Graph)(Circle Graph)

A Pie Chart would be appropriate here to see what percent of students choose each type of exercise

Pie Chart Pie Chart (Circle Graph)(Circle Graph)

1 student of 8 chose swimming: 1/8 = .125 (x 100 = 12.5%) (1/8 of the circle)

2 students out of 8 chose jogging: 2/8 x 100 = 25% (1/4 of the circle)

4 students out of 8 chose soccer: 4/8 x 100 = 50% (1/2 of the circle)

Slope of a LineSlope of a Line Slope is determined

using the formula:

Two points are selected on the line. The coordinates of those points are taken.

Two points: (2, 3) and (4, 9)

point 1 coordinates and point 2 coordinates

so:

(2, 3) and (4, 9) 9-3 = 6 = 3 4-2 2

The slope of this line is 3.

X1, Y1 X2, Y2

Slope of a LineSlope of a Line What is the slope of

this line? Let’s call R point 1 and

S point two. R coordinates: (1, 6)

S coordinates: (4, 12)

Slope =

X1, Y1

X2, Y2

12 - 6 = 6 = 2 4 - 1 3