Analyzing Categorical Data

&

Displaying Quantitative DataSection 1.1 & 1.2

Reference Text:

The Practice of Statistics, Fourth Edition.

Starnes, Yates, Moore

Starter Problem

• Antoinette plays a lot of golf. This summer she got a new driver and kept track of how far she hit her tee shots in several rounds. Look at these data (drive lengths in yards) and then write a few sentences that describe the lengths of her drives:

246 260 230 233 254 203 223 193 238 220 210 237

270 240 192 204 250 274 220 240 235 250 222

230 225 241 225 230 250 200 250 226 240

Today’s Objectives• Analyze pie charts and bar graphs

• Two way tables:– Marginal Distribution

– Conditional Distribution

• A Titanic Disaster

• Analyze Dot Plots

• Describe CUSS your new best friend

• Stem and Leaf Plots: single, and back to back

• Histograms

California Standard 14.0

Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.

Types of Variables• Categorical variables record which group or

category an individual belongs to.– What color is your hair?

– What year are you in school?

– What city do you live in?

– Did the tee shot land in the fairway?

– It does NOT make sense to average the results.

• Quantitative variables take on numeric values.– How tall is a person?

– What score did a person get on the SAT?

– How many desks are in a room?

– How long was the tee shot?

– It DOES make sense to average the results.

Visual Representation of

Categorical Variables

• Categorical variables are

typically represented by

pie charts (for percents)

or bar charts (percents or

counts).

0

50

100

150

S M W D

Millions

Single

Married

Widowed

Divorced

Married? Count (M) Percent

Single 41.8 22.6

Married 113.3 61.1

Widowed 13.9 7.5

Divorced 16.3 8.8

Dilbert comics

Use a pie chart only when you want to

emphasize each category’s relation to the

whole. Pie charts are awkward to make by

hand, but technology will do the job for you.

What Makes a Good Bar

Graph?

• Good– All bars have the same

width

– X & Y axis’ labeled

– Units

– Title of Graph

• Bad– Bars have different

widths

– Pictures replacing the

bars

– No labels

– Turn to Pg 11 in Text

Two Way Tables

• Marginal Distribution

– The marginal distribution of one of the

categorical variables in a two way table of

counts is the distribution of values of that

variable among all individuals described by

the table

– For example: data that has both Male and Female

data, marginal dist. would be just looking at males

compared to EVERYONE

– Example: Pg 12

Two Way Tables

• Conditional Distribution

– A conditional distribution of a variable

describes the values of that variable among

individuals who have specific value of another

variable. There is a separate conditional dist.

For each value of the other variable.

– For Example: Male & Females, just looking at the

females and comparing the females amongst the

different categories.

– Example pg 14

A Titanic Disaster: Activity

– Please turn to page 19 in your text book

– What to do:

1) What is the percent of people who survived?

– Is this a marginal or conditional, write a complete

sentence!

2) Given the passenger survived, what are the

percentages for each class?

– Is this a marginal or conditional, write a complete

sentence!

3) Of those who died in first class, what percent of

them were males? Females?

Break!

- 5 Minutes

Section 1.2: Quantitative Data

w/ Graphs• Dotplots

• CUSS

• Histograms

• Stemplots

Types of Variables• Categorical variables record which group or

category an individual belongs to.– What color is your hair?

– What year are you in school?

– What city do you live in?

– Did the tee shot land in the fairway?

– It does NOT make sense to average the results.

• Quantitative variables take on numeric values.– How tall is a person?

– What score did a person get on the SAT?

– How many desks are in a room?

– How long was the tee shot?

– It DOES make sense to average the results.

Visual representation of

Quantitative Variables: Dotplots• The most basic method is a dotplot.

– Every data point can be seen on the plot.

• Construction method:– Draw a horizontal axis with a scale that covers the full range of

values for the variable.

– Put a dot on (or above) the axis for each data point.

– If data duplicate, stack them vertically.

• Construct a dotplot now of Antoinette’s drives:

246 260 230 233 254 203 223 193 238 220 210 237

270 240 192 204 250 274 220 240 235 250 222

230 225 241 225 230 250 200 250 226 240

Dotplot of Drive Data

• Based on the dotplot, estimate the center.

– We see it around 230 or 240 yards.

• Estimate the spread.

– Roughly from 190 to almost 280, so spread is about 90 yards.

• Describe the shape.

– It appears “mound-shaped” with most of the data clustered at the

center and with tails at each end.

CalDrives

200 220 240 260 280

Collection 1 Dot Plot

C.U.S.S• C: Center

• Median, where is it?

– Mean can also describe the center, but is not resistant…

• U: Unusual data points

• Outliers! Are there any? We can calculate them…later in 1.3

• S: Spread

• Describe the variability of the graph

– (largest value – smallest value)

• S: Shape

• How many peaks? Is the data clumped in a general location?

Is data stretching to the right (skewed right). Is the data

stretching to the left (skewed left).

• LASTLY…Always, ALWAYS C.U.S.S it out when

describing graphs of data

Histograms

• Another important method is a histogram.– Individual data points cannot be seen on the plot.

– Many data points are grouped together in vertical bars.

• Construction method:– Draw a horizontal axis with a scale that covers the full range of

values for the variable.

– Decide bar width (also called class width) so that 5 to 10 bars will cover the full range of data.

– Set borders for bars, count frequencies, draw bars.

– Use a vertical axis to show the bar height.

Histogram of Drive Data

Cou

nt

1

2

3

4

5

6

7

8

CalDrives

180 200 220 240 260 280 300

Collection 1 Histogram

• From a visual examination, estimate the center,

unusual points, spread and the shape. (CUSS)

– As before, you should see the center around 230 to

240, no unusual points, the spread looks like 90, and

the shape still looks like a mound.

StemplotsAKA: Stem & Leaf Plots

• One way to organize numerical data is to

make a stemplot.

• Lets turn to the board and walk through

how to make a stemplot of the following

data, found on pg 33

• 50 26 26 31 57 19 24 22 23 38

13 50 13 34 23 30 49 13 15 51

Stemplots check list

• Did we make a stemplot?

• Did we talk about splitting stems

– 1122334455… upper and lower bounds

• Did we talk about back to back stemplots?

• Good…now we can move on

Percent of Population Over 65 by State

4 9

5

6

7

8 8

9

10 0 0 2 9

11 0 1 1 3 4 4 4 6 9

12 0 0 3 4 4 5 5 5 6 6 6 6

13 0 1 3 3 4 4 5 6 7 7 9 9 9

14 2 3 4 5 5

15 2 3 7 9

16

17

18 6

Note: 4|9 = 4.9%

Today’s Objectives• Analyze pie charts and bar graphs

• Two way tables:– Marginal Distribution

– Conditional Distribution

• A Titanic Disaster

• Analyze Dot Plots

• Describe CUSS your new best friend

• Stem and Leaf Plots: single, and back to back

• Histograms

California Standard 14.0

Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.

Homework

Review pages 8-42 in the text.The Practice of Statistics, Fourth Edition. Starnes, Yates, Moore

• TB PG 22: 9, 11, 14,15,18,20

• TB PG 42: 37,45,49,59,62,69,70,72-74

• Herring’s Workbook PG 4&5

– Use 8.5x11 binder paper

– Follow homework guidelines