Understanding Graphs

Bar Graph Easy to make

Information is easily understood

Each bar represents counts for a category

The length of the bar represents the percent of the total that falls into that category

Bar Graphs

Favorite Pizza Toppings

05

10152025303540

ExtraCheese

Pepperoni Sausage Mushrooms

Toppings

Fre

qu

ency

x-axis

y-axistitle

labels

origin

Box-and-Whisker Plots Good for large data sets — at least 15

Give five important pieces of data: median, maximum, minimum, lower and upper quartiles

Can be used to compare sets with different number of data points

Box-and-Whisker Plots

Math Test Scores

median

maximumminimum

lower quartile upper quartile

title

number line

Easy to read

Each piece represents a percent of the whole

Can also calculate the degree of the circle

Shows the whole as 100 percent

Circle Graphs

Favorite Sport

Baseball36%

Basketball18%

Soccer18%

Football21%

Wrestling7%

Baseball

Basketball

Soccer

Football

Wrestling

Circle Graphs title

legendpercent of total

Histogram Kind of a bar graph

Easy to make

Bars represent an interval of data—not just one number (e.g., 0 to 5)

The length of the bar represents the number that falls into that category

Histogram

Hours Playing Video Games /Week

0

2

4

6

8

10

12

0-5 5.1-10 10.1- 15 15.1-20

Number of Hours

Nu

mb

er o

f S

tud

ents

title

label for x-axis

label for y-axis

interval of data for each category

Line Plots Easy to read

Easy to make

Best when you have 25 data points or less

Shows clusters (groups of points), gaps (large spaces between points), outliers (points much larger or smaller in value) and variability (how the data is spread)

Line Plots

Represents 1 cookie

title

Number line

Organizes bivariate data (two variables)

Shows the association between two variables

Involves causation and association

Shows clusters and outliers

Have the independent variable on the x-axis

Can only connect points in a time-series

Scatter Plots

Scatter Plots

McDonald's Sandwiches

0

200

400

600

800

1000

0 10 20 30 40 50

Grams of Fat

Cal

ori

es

title

Dependent variabley-axis

label for y-axis

label for x-axis

Independent variablex-axis

Stem-and-Leaf Plots

Easy to make

Best with more than 25 values

Allows the identification of largest and smallest values, clusters, gaps and outliers

Other varieties include back-to-back plots

Stem-and-Leaf Plot

Stems Leaves

01 2, 4,5,6,82 33 6

2|3 means 23

Legend

Measure of Center

Mean — A number that represents the middle point, or average.

It is the quotient obtained by dividing the sum total of a set of figures by the number of figures.

MeanMean Health Care Salaries

Surgeon $184,150

Home health aides

$20,960

Nurses aides $22,960

Dental assistants $30,850

Physical therapists

$41,410

Athletic trainers $38,860

• The sum of the salaries is $339,190

• There are six values.

• $339,160/6 = $56,531

• The mean is $56,531

Median — The value in an ordered set of values that represents the point of which there are as many instances higher as there are lower.

Measures of Center

MedianMean Health Care Salaries

Surgeon $184,150

Home health aides

$20,960

Nurses aides $22,960

Dental assistants $30,850

Physical therapists

$41,410

Athletic trainers $38,860

• Put the numbers in order by value:184,150 41,410 38,860 30,850 22,960 20,960

• Find the middle. In this case, the middle is between 38,860 and 30,850. So find the mean of those 38,860 + 30,850

2• $69,720/2 = 34,855

• The median is $34,855

Mode — The most frequent value of a set of data.

Measures of Center…continued

Mean Health Care Salaries

Surgeon $184,150

Home health aides

$20,960

Nurses aides $22,960

Dental assistants $30,850

Physical therapists

$41,410

Athletic trainers $38,860

• There is no number that appears most often, therefore:

• There is no mode.

The mean is $56,531. The median is $34,855. There is no mode.Why are the mean and the median so

different if they are both measures of center?

The mean is greatly affected by very large or very small numbers. The surgeon’s salary is much greater than the others and that gives us a larger mean.

Look at the measures of center

For more information about data, go to

Quiz Bus: Dealing With Data http://westernreservepublicmedia.org/quizbus/index.htm

Dealing With Data Hotlist http://westernreservepublicmedia.org/quizbus/index.htm

Understanding Graphs