Third Edition Chapter 2: Describing Location in a...

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The Practice of Statistics Third Edition Chapter 2: Describing Location in a Distribution Copyright © 2008 by W. H. Freeman & Company

Transcript of Third Edition Chapter 2: Describing Location in a...

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The Practice of StatisticsThird Edition

Chapter 2:Describing Location in a Distribution

Copyright © 2008 by W. H. Freeman & Company

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Data Analysis Toolbox

• Data – Organize & Examine

– Who, What, Why, Where, When, How, & by Whom

•W5HW

• Graphs – Appropriate Graphical Display

– Box plot, histogram, etc.

• Numerical Summaries – Relevant Statistics

• Interpretation – Answer the Question!!!

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Strategy for Single Variable Data

• To measure the relative standing in a

distribution.

– Plot the data.

– Look for pattern (Shape, Center, Spread)

to find deviations such as outliers.

– Calculate a numerical summary to

describe center and spread.

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• The overall pattern may be so

regular that we can describe it with

a smooth curve.

• Doing so allows us to describe the

locations of individual

observations within a distribution.

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947 Seventh Graders in Gary, Indiana on ITBS.

Regular distribution, tails fall off smoothly, single center peak,

no gaps or outliers.

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The Density Curve

• It is a mathematical model for the

distribution.

• An idealized description of the data.

• A compact picture of the overall pattern of

the data.

• Ignores minor irregularities and outliers.

• Easier to work with curve than histogram.

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Graph on left shows all the students with a score of 6 or less.

This is basically the 30th percentile. (.303)

Graph on right shows the area under the curve that is 6 or less.

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The area under the curve is equal to 1.

This blue area is actually .293, so very close to .303.

So using this DENSITY CURVE is a very good estimate of the

areas given by the histogram.

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This is a Density Curve That is Skewed Left.

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Remember no set of real data is EXACTLY described by a

density curve.

The curve is an approximation that is easy to use and accurate

enough for practical use.

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Measures of Center

We can eyeball the centers and the quartiles.

This is not true of Standard Deviation.

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Please Note

• We use x-bar (mean) and s (S.D.) with our

actual observations.

• Density Curve is an IDEALIZED

description of data.

• Therefore the mean of a density curve is

denoted by μ (the Greek letter mu)

• The standard deviation of a density curve is

noted by σ (Greek letter sigma).

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Assignment

• Exercises 2.7, 2.9, 2.10, 2.12, 2.13,

• Read pages 133- 136

• Watch: www.learner.org/courses/againstallodds/unitpages/unit07.html