Displaying Quantitative Data with Graphs

Chapter 1.2

Stemplots and Back-to-Back Stemplots

Quantitative Data Display When displaying Categorical Data we use Pie Charts

and/or Bar Graphs

To display qualitative data we use A. Dotplots

B. Stemplots

C. Histograms

D. Box Plots

When analyzing the data we will describe the overall pattern (Shape, Center, and Spread) of the distribution

A) Dotplot Small datasets with a small range (max-min) can be easily

displayed using a dotplot

Draw and Label a number line from min to max

Place one dot per observation above its value

Stuck multiple observations evenly

Describe Shape SOCS

I. Shape: peak, cluster, tail direction, symmetry and skewed distribution

II. Center: midpoint,

III. Spread: range min-max

IV. Outliers: stand out values from the overall distribution

S- Shape: Symmetry and Skew A distribution is roughly symmetric if the right and left sides of the

graph are approximately mirror images of each other.

A distribution is skewed to the right (right-skewed) if the right side of

the graph (containing the half of the observations with larger values) is

much longer than the left side.

It is skewed to the left (left-skewed) if the left side of the graph is

much longer than the right side.

Symmetric Skewed-left Skewed-right

Comparing Distributions In statistics we are mostly interested in Comparing

two or more groups.

Which diet of the two works best?

Which North American University should one attend?

What improves memory?

….and ofcourse

Who gets more detentions per year in CDS: girls or boys?

Compare the distribution of Household size for U.K. and South Africa. Don’t forget your SOCS

SHAPE?

CENTER (midpoint

)

SPREAD

OUTLIERS

TRY: Energy Cost Example Top VS Bottom Freezers

How do the annual energy costs (in dollars) compare for refrigerators with top freezers and refrigerators with bottom freezers? The data below are from the May 2010 issue of Consumer Reports.

Problem: Compare the distributions of energy cost for these two types of refrigerators.

EnergyCost

Ty

pe

14012611298847056

bottom

top

Dotplot of EnergyCost vs Type

B)

How MANY pairs of shoes does a typical teenager have?

Random sample of 20 students

In the case of males?

50 26 26 31 57 19 24 22 23 38

13 50 13 34 23 30 49 13 15 51

0

0

1

1

2

2

3

3

4

4

5

5

Key: 4|9

represents a

student who

reported

having 49

pairs of shoes.

Females

14 7 6 5 12 38 8 7 10 10

10 11 4 5 22 7 5 10 35 7

Males

0 4

0 555677778

1 0000124

1

2 2

2

3

3 58

4

4

5

5

Females

333

95

4332

66

410

8

9

100

7

Males

“split stems”

Back-to-Back Stemplots • When comparing use back-to-back stemplots • If data is bunched-up split stems

AP Exam Common Errors When describing a distribution students forget to

address all 4 characteristics of SOCS

When comparing not explicitly comparing the characteristics . Discussing the SOCS for each distribution separately WILL NOT give partial credit

Use phrases like “about the same as”

Is much greater than

When making stemplots: forgetting the Key or labels

TRY: Back-to-Back Stemplot

Male: 154, 157, 187, 163, 167, 159, 169, 162, 176, 177, 151,

175, 174, 165, 165, 183, 180

Female: 160, 169, 152, 167, 164, 163, 160, 163, 169, 157, 158,

153, 161, 165, 165, 159, 168, 153, 166, 158, 158, 166

Who’s Taller? Who is taller, males or females? A sample of 14-year-olds from the United Kingdom was randomly selected using the CensusAtSchool Web site. Here are the heights of the students (in cm):

TRY these ones:

Group Work: FRAPPY Evaluation!

Have fun!

Homework!!! 1. pg- 41

#37 - #49 odd

2. Must Bring your Graphing Calculator

3. Read ahead if you can: page 33-40