1. Section 1.1-1 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series by Mario F. Triola

2. Section 1.1-2 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Preview Polls, studies, surveys and other data collecting tools collect data from a small part of a larger group so that we can learn something about the larger group. This is a common and important goal of statistics: Learn about a large group by examining data from some of its members.

3. Section 1.1-3 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Preview In this context, the terms sample and population have special meaning. Formal definitions for these and other basic terms will be given here. In this chapter, we will look at some of the ways to describe data.

4. Section 1.1-4 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Chapter 1 Introduction to Statistics 1-1Review and Preview 1-2Statistical and Critical Thinking 1-3Types of Data 1-4Collecting Sample Data

5. Section 1.1-5 Copyright © 2014, 2012, 2010 Pearson Education, Inc.  Data - Collections of observations, such as measurements, genders, or survey responses Data

6. Section 1.1-6 Copyright © 2014, 2012, 2010 Pearson Education, Inc.  Statistics - The science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data Statistics

7. Section 1.1-7 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Population  Population - The complete collection of all measurements or data that are being considered

8. Section 1.1-8 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Census versus Sample  Census - Collection of data from every member of a population  Sample - Subcollection of members selected from a population

9. Section 1.2-9 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Potential Pitfalls – Misleading Conclusions 1-2  Concluding that one variable causes the other variable when in fact the variables are only correlated or associated together. Two variables that may seemed linked, are smoking and pulse rate. We cannot conclude the one causes the other. Correlation does not imply causality.

10. Section 1.3-10 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Chapter 1 Introduction to Statistics 1-1Review and Preview 1-2Statistical and Critical Thinking 1-3Types of Data 1-4Collecting Sample Data

11. Section 1.3-11 Copyright © 2014, 2012, 2010 Pearson Education, Inc.  Parameter a numerical measurement describing some characteristic of a population. population parameter Parameter

12. Section 1.3-12 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Statistic  Statistic a numerical measurement describing some characteristic of a sample. sample statistic

13. Section 1.3-13 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Quantitative Data  Quantitative (or numerical) data consists of numbers representing counts or measurements. Example: The weights of supermodels Example: The ages of respondents

14. Section 1.3-14 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Categorical Data  Categorical (or qualitative or attribute) data consists of names or labels (representing categories). Example: The gender (male/female) of professional athletes Example: Shirt numbers on professional athletes uniforms - substitutes for names.

15. Section 1.3-15 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Working with Quantitative Data Quantitative data can be further described by distinguishing between discrete and continuous types.

16. Section 1.3-16 Copyright © 2014, 2012, 2010 Pearson Education, Inc.  Discrete data result when the number of possible values is either a finite number or a ‘countable’ number (i.e. the number of possible values is 0, 1, 2, 3,...). Example: The number of eggs that a hen lays Discrete Data

17. Section 1.3-17 Copyright © 2014, 2012, 2010 Pearson Education, Inc.  Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps. Continuous Data Example: The amount of milk that a cow produces; e.g. 2.343115 gallons per day

18. Section 1.3-18 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Summary - Levels of Measurement  Nominal - categories only  Ordinal - categories with some order  Interval - differences but no natural zero point  Ratio - differences and a natural zero point

19. Section 1.4-19 Copyright © 2014, 2012, 2010 Pearson Education, Inc.  Random  Systematic  Convenience  Stratified  Cluster  Multistage Methods of Sampling – Summary 1-4

20. Section 2.1-20 Copyright © 2014, 2012, 2010 Pearson Education, Inc. 1. Center: A representative value that indicates where the middle of the data set is located. 2. Variation: A measure of the amount that the data values vary. 3. Distribution: The nature or shape of the spread of data over the range of values (such as bell-shaped, uniform, or skewed). 4. Outliers: Sample values that lie very far away from the vast majority of other sample values. 5. Time: Changing characteristics of the data over time. Preview Ch 2 Characteristics of Data

21. Section 2.3-21 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 2-3 Example IQ scores from children with low levels of lead. IQ ScoreFrequency 50-692 70-8933 90-10935 110-1297 130-1491

22. Section 2.3-22 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 2-3 Skewness A distribution of data is skewed if it is not symmetric and extends more to one side to the other. Data skewed to the right (positively skewed) have a longer right tail. Data skewed to the left (negative skewed) have a longer left tail.

23. Section 2.3-23 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Example – Discuss the Shape

24. Section 2.4-24 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 2-4 Pareto Chart A bar graph for qualitative data, with the bars arranged in descending order according to frequencies

25. Section 2.4-25 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 2-4 Pie Chart A graph depicting qualitative data as slices of a circle, in which the size of each slice is proportional to frequency count

26. Section 2.4-26 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 2-4 Frequency Polygon uses line segments connected to points directly above class midpoint values.

27. Section 2.4-27 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 2-4 Important Principles Suggested by Edward Tufte For small data sets of 20 values or fewer, use a table instead of a graph. A graph of data should make the viewer focus on the true nature of the data, not on other elements, such as eye-catching but distracting design features. Do not distort data. Construct a graph to reveal the true nature of the data. Almost all of the ink in a graph should be used for the data, not for the other design elements.

28. Section 3.1-28 Copyright © 2014, 2012, 2010 Pearson Education, Inc.  Descriptive Statistics In this chapter we’ll learn to summarize or describe the important characteristics of a data set (mean, standard deviation, etc.).  Inferential Statistics In later chapters we’ll learn to use sample data to make inferences or generalizations about a population. Ch 3 Preview

29. Section 3.3-29 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-3 Definition The standard deviation of a set of sample values, denoted by s, is a measure of how much data values deviate away from the mean.

30. Section 3.3-30 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-3 Sample Standard Deviation Formula

31. Section 3.3-31 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-3 Standard Deviation – Important Properties  The standard deviation is a measure of variation of all values from the mean.  The value of the standard deviation s is usually positive (it is never negative).  The value of the standard deviation s can increase dramatically with the inclusion of one or more outliers (data values far away from all others).  The units of the standard deviation s are the same as the units of the original data values.

32. Section 3.3-32 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-3 Example Use either formula to find the standard deviation of these numbers of chocolate chips: 22, 22, 26, 24

33. Section 3.3-33 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-3 Example

34. Section 3.3-34 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-3 Empirical (or 68-95-99.7) Rule For data sets having a distribution that is approximately bell shaped, the following properties apply:  About 68% of all values fall within 1 standard deviation of the mean.  About 95% of all values fall within 2 standard deviations of the mean.  About 99.7% of all values fall within 3 standard deviations of the mean.

35. Section 3.3-35 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-3 The Empirical Rule

36. Section 3.3-36 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch3-3 Coefficient of Variation The coefficient of variation (or CV) for a set of nonnegative sample or population data, expressed as a percent, describes the standard deviation relative to the mean. SamplePopulation

37. Section 3.4-37 Copyright © 2014, 2012, 2010 Pearson Education, Inc.  z Score (or standardized value) the number of standard deviations that a given value x is above or below the mean Ch 3-4 z score

38. Section 3.4-38 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Sample Population Round z scores to 2 decimal places Measures of Position z Score

39. Section 3.4-39 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Example The author of the text measured his pulse rate to be 48 beats per minute. Is that pulse rate unusual if the mean adult male pulse rate is 67.3 beats per minute with a standard deviation of 10.3? Answer: Since the z score is between – 2 and +2, his pulse rate is not unusual.

40. Section 3.4-40 Copyright © 2014, 2012, 2010 Pearson Education, Inc. 1.Find the 5-number summary. 2.Construct a scale with values that include the minimum and maximum data values. 3.Construct a box (rectangle) extending from Q1 to Q3 and draw a line in the box at the value of Q2 (median). 4.Draw lines extending outward from the box to the minimum and maximum values. Ch 3-4 Boxplot - Construction

41. Section 3.4-41 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-4 Boxplots

42. Section 3.4-42 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-4 Outliers  An outlier is a value that lies very far away from the vast majority of the other values in a data set.

43. Section 3.4-43 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Ch 3-4 Important Principles  An outlier can have a dramatic effect on the mean and the standard deviation.  An outlier can have a dramatic effect on the scale of the histogram so that the true nature of the distribution is totally obscured.

44. Section 3.4-44 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Putting It All Together  So far, we have discussed several basic tools commonly used in statistics –  Context of data  Source of data  Sampling method  Measures of center and variation  Distribution and outliers  Changing patterns over time  Conclusions and practical implications  This is an excellent checklist, but it should not replace thinking about any other relevant factors.