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Copyright © 2011 Pearson Education, Inc. Putting Statistics to Work
Copyright © 2011 Pearson Education, Inc. Slide 6-3 Unit 6A Characterizing Data
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-4 The distribution of a variable (or data set) describes the values taken on by the variable and the frequency (or relative frequency) of these values. Definition
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-5 The mean is what we most commonly call the average value. It is defined as follows: The median is the middle value in the sorted data set (or halfway between the two middle values if the number of values is even). The mode is the most common value (or group of values) in a distribution. Measures of Center in a Distribution
6-A You try it! Copyright © 2011 Pearson Education, Inc. Slide 6-6 The lengths (in minutes) of a sample of cell phone calls are shown: 61936128 Find the mean. A. 54 B. 9 C. 6 D. 7
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-7 Mean vs. Average
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-8 6.72 3.46 3.60 6.44 26.70 (data set) 3.46 3.60 6.44 6.72 26.70 (sorted list) (odd number of values) median is 6.44 exact middle Example: Find the median of the data set below. Finding the Median for an Odd Number of Values
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-9 6.72 3.46 3.60 6.44 (data set) 3.46 3.60 6.44 6.72 (sorted list) (even number of values) 3.60 + 6.44 2 median is 5.02 Example: Find the median of the data set below. Finding the Median for an Even Number of Values
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-10 Finding the Mode a. 5 5 5 3 1 5 1 4 3 5 b. 1 2 2 2 3 4 5 6 6 6 7 9 c. 1 2 3 6 7 8 9 10 Mode is 5 Bimodal (2 and 6) No Mode Example: Find the mode of each data set below.
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-11 Effects of Outliers An outlier is a data value that is much higher or much lower than almost all other values. Consider the following data set of contract offers: $0 $0 $0 $0 $2,500,000 The mean contract offer is As displayed, outliers can pull the mean upward (or downward). The median and mode of the data are not affected.
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-12 Two single-peaked (unimodal) distributions A double-peaked (bimodal) distribution Shapes of Distributions
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-13 Symmetry A distribution is symmetric if its left half is a mirror image of its right half.
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-14 A distribution is left- skewed if its values are more spread out on the left side. A distribution is right- skewed if its values are more spread out on the right side. Skewness
6-A Copyright © 2011 Pearson Education, Inc. Slide 6-15 Variation From left to right, these three distributions have increasing variation. Variation describes how widely data values are spread out about the center of a distribution.
6-A Assignment P. 379-380 7-37 odd Copyright © 2011 Pearson Education, Inc. Slide 6-16
Copyright © 2015, 2011, 2008 Pearson Education, Inc. Chapter 6, Unit A, Slide 1 Putting Statistics to Work 6.
Learning Goal: To be able to describe the general shape of a distribution in terms of its number of modes, skewness, and variation. 4.2 Shapes of Distributions.
Unit 6A Characterizing a Data Distribution. DISTRIBUTION The distribution of a variable (or data set) describes the values taken on by the variable and.
© 2008 Pearson Addison-Wesley. All rights reserved Chapter 6 Putting Statistics to Work.
Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Created by Tom Wegleitner, Centreville, Virginia Section 3-1 Review and.
Copyright © 2010, 2007, 2004 Pearson Education, Inc. Lecture Slides Elementary Statistics Eleventh Edition and the Triola Statistics Series by.
Slide 1 Statistics Workshop Tutorial 3 Measures of the Center Measures of Variation Empirical Rule Chebyshev’s Theorem.
Copyright © 2005 Pearson Education, Inc. Slide 6-1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5- 1.
Quantitative Analysis (Statistics Week 8) FDA B&M Level C Peter Matthews
Unit 3 Sections 3-2 – Day : Properties and Uses of Central Tendency The Mean One computes the mean by using all the values of the data. The.
IT Colleges Introduction to Statistical Computer Packages Lecture 3 Eng. Heba Hamad week
Slide Slide 1 Chapter 3 Statistics for Describing, Exploring, and Comparing Data 3-1 Overview 3-2 Measures of Center 3-3 Measures of Variation 3-4 Measures.
Copyright © 2011 Pearson Education, Inc. Putting Statistics to Work.
Probabilistic & Statistical Techniques Eng. Tamer Eshtawi First Semester Eng. Tamer Eshtawi First Semester
1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Measures of Center.
Multiple choice questions…grab handout!. Data Analysis: Displaying Quantitative Data.
Describing & Comparing Data Unit 7 - Statistics. Describing Data Shape Symmetric or Skewed or Bimodal Center Mean (average) or Median Spread Range.
Slide Slide 1 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Created by Tom Wegleitner, Centreville, Virginia Section 3-1.
Descriptive statistics Describing data with numbers: measures of location.
Slide 1 Copyright © 2004 Pearson Education, Inc. Descriptive Statistics summarize or describe the important characteristics of a known set of population.
Copyright © 2010, 2007, 2004 Pearson Education, Inc. Measures of Center.
© 2013 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems Introductory Statistics: Exploring the World through.
Created by Tom Wegleitner, Centreville, Virginia Section 2-4 Measures of Center.
Chapter 4 Histograms Stem-and-Leaf Dot Plots Measures of Central Tendency Measures of Variation Measures of Position.
2012 Pearson Education, Inc. Slide Chapter 12 Statistics.
How many times can you write statistics in a minute? By: Madeline Stenken and Tara Levine.
Copyright © 2010 Pearson Education, Inc. Slide
(Unit 6) Formulas and Definitions:. Association. A connection between data values.
2.3 Measures of Central Tendency Coach Bridges NOTES.
Tutorial: Understanding the normal curve. Next mouse click.
1 Measure of Center Measure of Center the value at the center or middle of a data set 1.Mean 2.Median 3.Mode 4.Midrange (rarely used)
Introduction Our daily lives often involve a great deal of data, or numbers in context. It is important to understand how data is found, what it means,
Central Tendency Introduction to Statistics Chapter 3 Sep 1, 2009 Class #3.
By the end of this lesson you will be able to explain/calculate the following: 1. Histogram 2. Frequency Polygons.
Data handling Thursday. Objectives for today Extending our knowledge of statistics – range, mode, median and the mean. mode rangeToday we are focusing.
Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Chapter Descriptive Statistics 2.
Chapter 4 Sampling Distributions and Data Descriptions.
LIS 570 Summarising and presenting data - Univariate analysis.
4.1 Measures of Center We are learning to…analyze how adding another piece of data can affect the measures of center and spread.
Combining Like Terms. Only combine terms that are exactly the same!! Whats the same mean? –If numbers have a variable, then you can combine only ones.
2 Summary Measures Arithmetic Mean Median Mode Describing Data Numerically Variance Standard Deviation Range Interquartile Range Geometric Mean Skewness.
Copyright © 2011 Pearson Education, Inc. Describing Numerical Data Chapter 4.
Numerical Measures of Central Tendency. Central Tendency Measures of central tendency are used to display the idea of centralness for a data set. Most.
Slide 3- 1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Active Learning Lecture Slides For use with Classroom Response Systems.
Statistics Unit Test Review Chapters 11 & /11-2 Mean(average): the sum of the data divided by the number of pieces of data Median: the value appearing.
Data Description Chapter 3. The Focus of Chapter 3 Chapter 2 showed you how to organize and present data. Chapter 3 will show you how to summarize.
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