Warm-up
*Finish the Titanic Activity!
Numerical Graphs
Graphs to use for Quantitative
Data
Section 1.2
Analyzing Numerical Data
Learning Objectives
After this section, you should be able to…

DESCRIBE numerical graphs

CONSTRUCT & INTERPRET dot plots

CONSTRUCT & INTERPRET stem-plots
Describing a Graph

There’s a general strategy for interpreting
graphs of quantitative data.

Look for the overall pattern and for striking
departures from that pattern.
Describing a Graph –
Numerical Graphs Only!!!!!

Overall Pattern Described by:
a) Shape
Don’t forget your
b) Center
SOCS!
c) Spread

Departure Described by: Outlier
Outlier – An individual value that falls
outside the overall pattern.
Center
If you had to pick a single number to describe
all the data – the center would be the best.
It’s in the middle!
Shape Description
Concentrate on Main Features:




Look for Major Peaks – not minor ups and
downs
Look for clusters and obvious gaps
Look for possible outliers
Look for symmetry or skewness
Shape – Are there modes?
Unimodal
Bimodal
How many bumps are in the graph? – Those are modes.
UNIMODAL – A Distribution
that has 1 mode.
Remember – it will not
ALWAYS be EXACTLY the
same frequencies, but
they will be very close.
Symmetric?
Can you fold it along a vertical line through
the middle and have the edges math pretty
closely? If so, then it’s symmetric.
Bell-Shaped
Shape –Skewed?
It’s skewed to the side of the longer tail.
Negatively Skewed or
(Skewed left)
Positively Skewed or
(Skewed right)
For his own safety, which way should
he go “skewing?” Left of Course!
Shape – Unusual Features

Are there any
stragglers, or outliers?

Are there any gaps?
Spread – (Variation)
•
How spread out is the data?
(What is the Range?)
•
How spread out is the interquartile range?
(We will learn more about this later……..)
•
Is it tightly clustered around the center or
spread out?
We looked at the base salaries of the
CEOs of the 800 largest corporations
in 1994.

Center – Centered around
$500,000

Shape – Unimodal, Nearly
Symmetric, Some high outliers

Spread – Majority are between
$100,000 and 1,000,000. But
there are a few with salaries
between $2,500,000 and
$3,000,000
One of the simplest graphs to construct and interpret is a
dotplot. Each data value is shown as a dot above its
location on a number line.
How to Make a Dotplot
1)Draw a horizontal axis (a number line) and label it with the
variable name.
2)Scale the axis from the minimum to the maximum value.
3)Mark a dot above the location on the horizontal axis
corresponding to each data value.
Number of Goals Scored Per Game by the 2004 US Women’s Soccer Team
3
0
2
7
8
2
4
3
5
1
1
4
5
3
1
1
3
3
3
2
1
2
2
2
4
3
5
6
1
5
5
1
1
5
Displaying Quantitative Data

+
 Dotplots
EPA Estimate of Hwy Gas Mileage (mpg) for 24
2009 midsize cars.
Describe the shape, center, and
spread of the distribution.
- There are 3 clusters of values: cars that get 25 mpg,
28 – 30 mpg, and 33 mpg.
- Large Gaps between 22 mpg, 18 mpg, and 14 mpg.
- The center is about 28 mpg. (A typical 2009 model gets
28 mpg)
- Spread: Highest value is 33 mpg. Lowest value is 14
mpg. Range = 19 mpg.
- Outliers: There are 2 cars with unusually low gas
mileage ratings. These cars are possible outliers.
Dotplots
How many keys are on your keychain?
Dotplots – You Try one!
The following data give the number of hurricanes that
happened each year from 1944 through 1969.
3, 2, 1, 2, 4, 3, 7, 2, 3, 3, 2, 5, 2
These data represent the responses of 20 female AP
Statistics students to the question, “How many pairs of
shoes do you have?” Construct a stemplot.
50
26
26
31
57
19
24
22
23
38
13
50
13
34
23
30
49
13
15
51
1
1 93335
1 33359
2
2 664233
2 233466
3
3 1840
3 0148
4
4 9
4 9
5
5 0701
5 0017
Stems
Add leaves
Order leaves
Key: 4|9
represents a
female student
who reported
having 49
pairs of shoes.
Add a key
Displaying Quantitative Data

(Stem-and-Leaf Plots)
+
 Stemplots
Stemplot – (Stem & Leaf) –
Let’s find our pulse
rates.
What’s your height? Compare.
Male
Female
Sometimes we have to
truncate the data.
145
378
630
317
287
572
547
228
122
564
231
279
138
238
444
209
Grade Point Average
3.4
4
3.9
2.1
2.2
3.8
2.7
2.8
2.9
1.9
3.2
2.1
How Long is a Minute
Make & Describe a Stemplot
229
246
320
214
197
347
202
247
198
360
218
406
223
628
347
260
414
276
261
196
Homework

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