Warm-up

*Finish the Titanic Activity!

Numerical Graphs

Graphs to use for Quantitative Data

Section 1.2Analyzing Numerical Data

After this section, you should be able to…

DESCRIBE numerical graphs

CONSTRUCT & INTERPRET dot plots

CONSTRUCT & INTERPRET stem-plots

Learning Objectives

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

b) Center

c) Spread

Departure Described by: Outlier

Outlier – An individual value that falls

outside the overall pattern.

Don’t forget your SOCS!

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 downsLook for clusters and obvious gapsLook for possible outliersLook 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?

• How spread out is the interquartile range?

• Is it tightly clustered around the center or spread out?

(What is the Range?)

(We will learn more about this later……..)

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

+

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.

Displaying Q

uantitative Data

Dotplots 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

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

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

+Displaying Q

uantitative Data

Stemplots (Stem-and-Leaf Plots) 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

Stems

1

2

3

4

5

Add leaves

1 93335

2 664233

3 1840

4 9

5 0701 Order leaves

1 33359

2 233466

3 0148

4 9

5 0017 Add a key

Key: 4|9 represents a female student who reported having 49 pairs of shoes.

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

229 247 347

246 198 260

320 360 414

214 218 276

197 406 261

347 223 196

202 628

Homework

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