Math 81 – Graphing

Cartesian Coordinate System Plotting Ordered Pairs (x, y)

• (x is horizontal, y is vertical)

• center is (0,0)

Ex 1. Plot and indicate which quadrant they’re in.

A (0,2) B (3, 5) C (-2, -4) D (4, -2)

Quadrants: I (positive, positive)

II (negative, positive)

III (negative, negative)

IV (positive, negative)

Each increment is normally one UNLESS it is marked

(or labeled) differently.

Ex 2. Write coordinates of the points to the left.

Scatterplots – Individual points that are plotted in the xy-plane.

Ex 3. Make a scatterplot by plotting the given points. Be sure to label each axis.

(0,-3) (-2, 1) (2,2) (-4, -4)

Ex 4. Make a scatterplot by plotting the given points. Be sure to label each axis.

X | 1 2 3 4 5

Y | 2 3 1 5 4

Line Graphs – A scatterplot where the points are connected. They are often used to predict trends.

Ex 5. Make a line graph by plotting the given points. Be sure to label each axis.

(0,-3) (-2, 1) (2,2) (-4, -4)

Ex 6. Make a line graph by plotting the given points. Be sure to label each axis.

X | 1 2 3 4 5

Y | 2 3 1 5 4

Ex 7. Make a line graph by plotting the given points. Be sure to label each axis.

US internet users, U (in millions) in year Y.

Y | 2001 2002 2003 2004 2005

U | 143 158 162 189 201

a) Make a line graph (label axis and units)

b) Give any trends

If the points in a line graph pretty much follow a straight line, they are called collinear.

PICTOGRAPHS

Ice Cream Sold

Vanilla

Chocolate

Strawberry

Chocolate Peanut Butter

Twist

Key: Each = 50

Each = 25

Ex 8.

a) How many chocolate ice cream cones were sold?

b) How many strawberry ice cream cones were sold?

c) What flavor of cone sold the least?

d) What is the difference between how many chocolate cones and how many peanut butter cones

were sold?

e) How many cones were sold in all?

Black

Gray

Blue

Red

White

Green

Key: Each = 10

Each = 5

Ex 9.

a) What is the value of a whole car?

b) What color of car is most popular? Least popular?

c) How many people like red cars?

d) How many people like white cars?

e) What is the average number of people who like either gray or red cars?

Color of Car

= 10

= 5

What is the value of a whole car?

What color of car is most popular? Least popular?

How many people like red cars?

ople like white cars?

What is the average number of people who like either gray or red cars?

Ex 10. Hours Victoria Reads

Sunday 4

Monday 2

Tuesday 3

Wednesday 1

Thursday 2.5

Friday 0.5

Saturday 1.5

Choose a picture to represent hours, then decide how to make ½ a picture. When drawing the

pictographs be sure to be accurate and label correctly.

a) Make a pictograph horizontally

b) Make a pictograph vertically

Bar Graphs – give similar information as pictographs except the information is given in a bar.

Each bar is separated from the next bar by a space. The graph can be horizontal or vertical.

Ex 11.

a) What does the horizontal bar represent?

b) What does the vertical bar represent?

c) What is the favorite sport of 5th graders?

d) How many students like tennis best?

e) How many students like either gymnastics or baseball best?

f) How many students are in 5th grade?

g) What fraction of 5th graders like soccer best?

This is the same graph given in horizontal form (although we should write soccer and basketball).

Ex 12.

a) What day did Courtney do the most situps?

b) What day did she do the least?

c) How many situps did she do on Friday?

d) On which 2 days did Courtney do the same amount of situps?

Ex 13. Draw a bar graph using the following information about students’ pets.

What should the scale start at?

What are the labels for the graph?

Type of Pet Number of Pets

Bird 4

Horse 2

Dog 12

Fish 6

Cat 8

Histograms – used for variables whose values are numerical and measured on an interval scale. It is

generally used when dealing with large sets of data.

Differs from a vertical bar graph

• Usually a histogram will have bars of equal width, because the class intervals vary in size.

• Each interval contains values between the endpoints of the bars.

• The height of the bars corresponds to the frequency of the class it represents.

• The endpoints of the bars are labeled instead of the center of the bars.

• The bars touch one another.

Ex 14. Distribution of salaries of the Acme Corporation

a) How many employees earn between $ 44, 000 and $55,000?

b) How many employees earn below $22,000 a year?

c) How many employees earn between $33,000 and $66,000?

d) How many more adults earn $44,000 - $54,000 than earn $11,000 - $21,000?

e) How many employees work for the Acme corporation?

f) What ratio of the employees earn $22,000 - $32,000?

g) How many employees earn less than $88,000?

h) What ratio of the employees earn less than $88,000?

Ex 15. Data to graph

20 35 39 26 32 39 21

23 33 25 23 33 37 22

26 31 37 39 21 27 18

a) If we had class intervals of size 5, how many pieces of data would fall in the interval 30 – 34?

b) How many would be in the class interval 20 – 24?

Circle Graphs

Ex 16.

a) If their budget is $3000 per month, find the cost of each sector of the graph.

b) Use the graph to find where most of the Milton’s income is spent.

c) What is the ratio of their food budget to their entire budget?

d) What is the ratio of their rent budget to their food budget?

e) What is the ratio of their food budget to their rent budget?

f) What percent of their budget is devoted to miscellaneous and clothing?

g) What is the smallest part of their budget?

Ex 17. Methods of getting to school

Go to School # Students Fraction of Whole Decimal Fraction

School bus 58

Car 7

Walk 35

Bicycle 12

Public Bus 18

Other 0

Lying With Statistics

Ex 18. Which “average” is being used?

Person John Ann Bob Mary Sue Ted Carol

Money 3 1 10 5 2 999 2

Mean – (Add up and divide by the total number of people) – $146

Median – (The middle when lined up small to large) – $3

Mode – (The value which appears most often) – $2

Ex 19. What is the scale? This graph is pretty worthless without a vertical scale.

Ex 20. stretching or shirking the vertical axis can make the data “appear” differently.

All 3 graphs represent the same information. Graph 2 is trying to make Ann’s pumpkin appear much

larger than the others, and graph 3 is trying to make all 3 pumpkins appear close in size.

Ex 21. Newspapers and magazines like to use colorful pictures to represent public opinion and survey

responses. However, often times the pictures are too simple to give meaningful information. Take this

example:

This map shows how people in different states of the US like pizza.

The color code is

Red – love pizza

Yellow – like pizza

purple – hate pizza

That's all the information we have. The map really doesn't say very much. We don't know how it was

determined that people like pizza...were people asked if they liked pizza? Were people asked how much

pizza they ate in a week? a month? a year? Was the number of pizzas purchased at stores in different

states counted? Was the number of pizza restaurants in different states counted?

We also do not know if there are any real differences between how much people like pizza in the

different states. How much do people love pizza in California? What is the difference between how

much people love pizza in Utah compared to how much they like pizza in Nevada? There are no scales or

measurements to indicate any of this information. Although this type of graphic gives almost no

information, it is used frequently in many popular magazines.

Ex 22.

Presumably this graph shows that there were a bit more than 10 frogs in May and something like 40

frogs in September. However, because the frog picture is not regular (and lacks clear and distinct start

and stop points) it is impossible to read precise values from the chart. At face value the chart suggests

that frogs were simply bigger in September than in May... The title may correct that false impression,

but still leave the impression of a much bigger change. The frog on the right is about 3× longer and 3×

wider than the frog on the left and hence takes up 32=9 times more area (and presumably the eye

judges 33=27 times more mass and volume). Thus this sort of diagram leaves the viewer with a distorted

view of the actual data: a change much larger than a factor of 3.

We can be a bit more accurate with a pictograph.