QUANTITATIVE DATA chapter 4 (NUMERICAL). Slide 4- 2 Categorical variables “qualitative” (also called “qualitative”) Data that are NOT numerical or… makes

QUANTITATIVE DATA

chapter 4

(NUMERICAL)

Slide 4- 2

Categorical variablesCategorical variables(also called “qua“quallitative”itative”)Data that are NOT numerical or…Data that are numbers, but makes makes no sense to take an averageno sense to take an averagesuch as…

phone number… student ID number…

zip code… etc.

Slide 4- 3

Numerical variablesNumerical variables(also called “qua“quantntitative”itative”)makes sense to averagemakes sense to averagetwo types:

discrete & continuousdiscrete & continuous

Slide 4- 4

Discrete Discrete (numerical)(numerical)List-able set of values

usually countscounts of itemsexample: number of students in a class

grades on a test

price of gas (per gallon)

Slide 4- 5

ContinuousContinuous (numerical) (numerical) data can take on any values any values in the

domain of the variable usually measurementsmeasurements of somethingexamples: - thickness of cell phones

- temperature- amount of time you’ve been alive

(NO LIMIT to number of decimal places for possible values)

Identify the following variables:Identify the following variables:the cost of your last cell phone bill

the color of cars in the teacher’s lot

the number of text messages that you sent last week

the zip code of an individual

a person’s mass in kilograms

DISCRETE NUMERICAL

NUMERICAL, DISCRETE

NUMERICAL, CONTINUOUS

CATEGORICAL

CATEGORICAL

DotplotsDotplots

1.0 2.0 3.0 4.0Number

Pick a "random" number Dot Plot

Dot plots work well for relatively small relatively small data sets (50 or less)(50 or less)

Dot plots work well for relatively small relatively small data sets (50 or less)(50 or less)

MPG15 20 25 30 35 40 45 50

Highway MPG Dot Plot

Slide 4- 8

What’s wrong with this picture?!!What’s wrong with this picture?!!

Too much data Too much data for a dot plotfor a dot plot!!

FYGPA0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

SATGPA Dot Plot

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FYGPA0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

SATGPA Histogram

The histogram works The histogram works much better!much better!

DOTPLOT of test scores

Test155 60 65 70 75 80 85 90 95 100 105

Pre-AP Algebra II Dot Plot

How to read a HISTOGRAM

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Test155 60 65 70 75 80 85 90 95 100 105

Pre-AP Algebra II Histogram

2 test scores were≥100 but <105

3 test scores were≥65 but <70

Slide 4- 11

Changing a histogram’s BIN WIDTH

0 5 10 15 20 25 30 35hair_length (inches)

AP Statistics Classes at McNeil High School, 2011-12 Dot Plot

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AP Statistics Classes at McNeil High School, 2011-12 Histogram

bin width = 0.5bin width = 0.5

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HISTOGRAM vs BAR GRAPHS

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Test155 60 65 70 75 80 85 90 95 100 105

Pre-AP Algebra II Histogram

HISTOGRAMSare for NUMERICAL data

BAR GRAPHS are for CATEGORICAL data

Spread Spread (min & max values)(min & max values)

CUSSCUSS and and BSBSCenter Center (modes)(modes)

Unusual Features Unusual Features (gaps, possible outliers)(gaps, possible outliers)

Shape Shape (symmetric? skewed? uniform?)(symmetric? skewed? uniform?)

and and Be SpecificBe Specific!!

(describing distributions)(describing distributions)

Slide 4- 14

A A unimodalunimodal histogram…histogram…

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FYGPA0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

SATGPA Histogram

Slide 4- 15

A A bimodalbimodal histogram has two apparent peaks:histogram has two apparent peaks:

Slide 4- 16

A histogram in which all the bins (bars) are

about the same height is called uniformuniform..(say “roughly uniform”)

Slide 4- 17

ShapeShapeIs the histogram symmetricsymmetric?

ALWAYSALWAYS say “approximatelyapproximately symmetric” or “roughlyroughly symmetric”(unless it truly is perfectlyperfectly symmetric)

Slide 4- 18

Skewed to the left/rightSkewed to the left/rightThe thinner ends of a distribution are called tailstails.

Skewed to the left Skewed to the right(to the lower “numbers”) (to the higher “numbers”)

Slide 4- 19

Anything Unusual? Anything Unusual? The following histogram has possiblepossible outliers outliers—

there are three cities in the leftmost bin:

It’s a good idea to say It’s a good idea to say “possible” outliers. “possible” outliers. Next time we will learn Next time we will learn how to test for outliers.how to test for outliers.

It’s a good idea to say It’s a good idea to say “possible” outliers. “possible” outliers. Next time we will learn Next time we will learn how to test for outliers.how to test for outliers.

Slide 4- 20

CUSSing & BS-ing practiceCUSSing & BS-ing practice

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Quiz30 40 50 60 70 80 90 100 110

Collection 1 Histogram• Center: This distribution of quiz scores appears to have two modes, one at around 55, and another at around 80.

• Shape: The shape is bimodal, and around each mode the shape is roughly symmetric.

• Spread: The spread is from the mid-30’s to the mid-90’s.

• Unusual features: There is a gap in the lower 40’s, with a possible outlier in the mid 30’s.

Slide 4- 21

more CUSSing & BS-ing…more CUSSing & BS-ing…

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Grades60 70 80 90 100

Collection 1 Histogram• Center: This distribution of grades has a single mode at around 100.

• Shape: The shape is unimodal and skewed to the left (to the lower grades)

• Spread: The spread is from the mid-50’s to about 100.

• Unusual features: There is a gap from the upper 50’s to the upper 60’s, with a possible outlier in the mid 50’s.

this does NOT mean this does NOT mean that someone had a that someone had a grade of above 100.grade of above 100.(more likely, a lot of 98’s (more likely, a lot of 98’s and/or 99’s)and/or 99’s)

this does NOT mean this does NOT mean that someone had a that someone had a grade of above 100.grade of above 100.(more likely, a lot of 98’s (more likely, a lot of 98’s and/or 99’s)and/or 99’s)

Slide 4- 22

Comparing DistributionsComparing Distributions

CompareCompare the following distributions of ages for female and male heart attack patients.

Slide 4- 23

Comparing DistributionsComparing DistributionsBe sure to use language of Be sure to use language of

comparisoncomparison..•Center:Center: This distribution of ages for females has a higher center (at around 78) than the distribution for male patients (around 62).•Shape:Shape: Both distributions are unimodal. The distribution for males is nearly symmetric, while the distribution for females is slightly skewed to the lower ages.

Slide 4- 24

Comparing DistributionsComparing Distributions• Spread:Spread: Both distributions

have similar spreads: females from around 30 – 100, and males from about 24 – 96. Overall, the distribution for female ages is slightly higher than that for male ages.

• (There are no unusual unusual featuresfeatures)

• YOU MUST USE YOU MUST USE COMPLETE COMPLETE SENTENCES!!!SENTENCES!!!

STEM PLOTS

U.S. Presidents – Stem & Leaf PlotU.S. Presidents – Stem & Leaf PlotMake a stem & leaf plot of age of…Make a stem & leaf plot of age of…

U.S. PresidentsU.S. Presidents

meansage 43 at inaugurationage 46 at death

6*

43

U.S. PresidentsU.S. Presidents

(looks like a histogram!)(looks like a histogram!)

Slide 4- 29

Horsepower of cars reviewed by Consumer Reports:

(not always necessary (not always necessary to use split stems)to use split stems)

Slide 4- 30

Use stemplotsstemplots for small to fairly small to fairly moderatemoderate sizes of data (25 – 100)

Try to use graph paper graph paper (or make sure make sure that your numbers line upline up)

(this is okay…)(this is okay…) (this is NOT)(this is NOT)

Documents

QUANTITATIVE DATA chapter 4 (NUMERICAL). Slide 4- 2 Categorical variables “qualitative” (also called “qualitative”) Data that are NOT numerical or… makes