Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 14.4, Slide 1 14 Descriptive Statistics What a Data Set Tells Us.

Slides:

Advertisements

Similar presentations

15.4 The Normal Distribution Objectives:

Advertisements

Standard Scores Standard scores, or “z- scores” measure the relation between each score and its distribution.

AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a b c )Without calculating,

Active Learning Lecture Slides For use with Classroom Response Systems Probability Distributions.

14.4 The Normal Distribution

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.3, Slide 1 Set Theory 2 Using Mathematics to Classify Objects.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.1, Slide 1 Set Theory 2 Using Mathematics to Classify Objects.

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 14.1, Slide 1 14 Descriptive Statistics What a Data Set Tells Us.

In 2009, the mean mathematics score was 21 with a standard deviation of 5.3 for the ACT mathematics section. ReferenceReference Draw the normal curve in.

Copyright © 2011 Pearson Education, Inc. Putting Statistics to Work.

Chapter 13 Section 7 – Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Copyright © 2012 by Nelson Education Limited. Chapter 4 The Normal Curve 4-1.

Normal Curve 64, 95, 99.7.

© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 13-5 The Normal Distribution.

Chapter 6 Foundations of Educational Measurement Part 1 Jeffrey Oescher.

Normal Curves and Sampling Distributions Chapter 7.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1.

Slide Copyright © 2009 Pearson Education, Inc. AND Active Learning Lecture Slides For use with Classroom Response Systems Chapter 13 Statistics.

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 11.5 Lines and Curves in Space.

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. Chapter 6 Probability Distributions Section 6.2 Probabilities for Bell-Shaped Distributions.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, Slide Logic The Study of What’s True or False or Somewhere in Between.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, Slide Logic The Study of What’s True or False or Somewhere in Between.

Dr. Fowler  AFM  Unit 8-4 The Normal Distribution

Copyright © 2012 Pearson Education, Inc. All rights reserved Chapter 9 Statistics.

MATH 110 Sec 14-4 Lecture: The Normal Distribution The normal distribution describes many real-life data sets.

Thinking Mathematically Statistics: 12.4 The Normal Distribution.

Educational Research: Competencies for Analysis and Application, 9 th edition. Gay, Mills, & Airasian © 2009 Pearson Education, Inc. All rights reserved.

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 14.1, Slide 1 14 Descriptive Statistics What a Data Set Tells Us.

Slide Copyright © 2009 Pearson Education, Inc. AND Active Learning Lecture Slides For use with Classroom Response Systems Chapter 13 Statistics.

Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 16 Mathematics of Normal Distributions 16.1Approximately Normal.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.2, Slide 1 Set Theory 2 Using Mathematics to Classify Objects.

Section 2 Standard Units and Areas under the Standard Normal Distribution.

Chapter Normal Probability Distributions 1 of 25 5  2012 Pearson Education, Inc. All rights reserved.

Introduction to Normal Distributions

Chapter 5 Normal Probability Distributions.

Normal Distributions and the Empirical Rule

Descriptive Statistics: Numerical Methods

5.3 The Central Limit Theorem

Statistics 4/26 Objective: Students will be able to find measures of statistical dispersion. Standards: 1.02 Summarize and analyze univariate data to solve.

Chapter 12 Statistics 2012 Pearson Education, Inc.

8.1 Sampling Distributions

Chapter 2: Modeling Distributions of Data

Elementary Statistics: Picturing The World

Unit 1 - Day 1 Introduction to

ANATOMY OF THE EMPIRICAL RULE

Given the following data

5.3 The Central Limit Theorem

NORMAL PROBABILITY DISTRIBUTIONS

12/1/2018 Normal Distributions

Aim: what is the normal distribution?

Empirical Rule MM3D3.

Year-3 The standard deviation plus or minus 3 for 99.2% for year three will cover a standard deviation from to To calculate the normal.

Section 2.1 Density Curves & the Normal Distributions

Descriptive Statistics

Chapter 6: Normal Distributions

Quantitative Methods PSY302 Quiz Normal Curve Review February 6, 2017

The Normal Distribution

Section 2.1 Density Curves & the Normal Distributions

Empirical Rule Empirical rule only works for a bell-shaped distribution. That is, empirical rule cannot be applied to other distributions such as left-skewed,

Use the graph of the given normal distribution to identify μ and σ.

Chapter 3 Modeling Distributions of Data

5.3 The Central Limit Theorem

Chapter 3: Modeling Distributions of Data

Introduction to Normal Distributions

Section 2.5 notes continued

Chapter 5 Normal Probability Distributions.

Basic Practice of Statistics - 3rd Edition The Normal Distributions

Introduction to Normal Distributions

Presentation transcript:

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 14.4, Slide 1 14 Descriptive Statistics What a Data Set Tells Us

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 14.4, Slide 2 The Normal Distribution 14.4 Understand the basic properties of the normal curve. Relate the area under a normal curve to z -scores. Make conversions between raw scores and z -scores. Use the normal distribution to solve applied problems.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 3 The Normal Distribution The normal distribution describes many real-life data sets. The histogram shown gives an idea of the shape of a normal distribution.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 4 The Normal Distribution

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 5 The Normal Distribution We represent the mean by μ and the standard deviation by σ.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 6 Example: Suppose that the distribution of scores of 1,000 students who take a standardized intelligence test is a normal distribution. If the distribution’s mean is 450 and its standard deviation is 25, The Normal Distribution (continued on next slide) a) how many scores do we expect to fall between 425 and 475? b) how many scores do we expect to fall above 500?

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 7 Solution (a): 425 and 475 are each 1 standard deviation from the mean. Approximately 68% of the scores lie within 1 standard deviation of the mean. We expect about 0.68 × 1,000 = 680 scores are in the range 425 to 475. The Normal Distribution (continued on next slide)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 8 Solution (b): We know 5% of the scores lie more than 2 standard deviations above or below the mean, so we expect to have 0.05 ÷ 2 = of the scores to be The Normal Distribution above 500. Multiplying by 1,000, we can expect that * 1,000 = 25 scores to be above 500.