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Lecture Slides

Lecture Slides. Elementary Statistics Twelfth Edition and the Triola Statistics Series by Mario F. Triola. 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.

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Lecture Slides

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  1. Lecture Slides Elementary StatisticsTwelfth Edition and the Triola Statistics Series by Mario F. Triola

  2. 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. 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. Chapter 1Introduction to Statistics 1-1 Review and Preview 1-2 Statistical and Critical Thinking 1-3 Types of Data 1-4 Collecting Sample Data

  5. Data - Collections ofobservations, such as measurements, genders, or survey responses Data

  6. 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. Population - The complete collection of all measurements or data that are being considered Population

  8. Census versus Sample • Census - Collection of data from every member of a population • Sample - Subcollection of members selected from a population

  9. 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. Potential Pitfalls – Misleading Conclusions 1-2

  10. Chapter 1Introduction to Statistics 1-1 Review and Preview 1-2 Statistical and Critical Thinking 1-3 Types of Data 1-4 Collecting Sample Data

  11. Parameter a numerical measurement describing some characteristic of a population. Parameter population parameter

  12. sample statistic Statistic • Statistic • a numerical measurement describing some characteristic of a sample.

  13. Quantitative Data • Quantitative (or numerical) data • consists of numbers representing counts or measurements. • Example: The weights of supermodels • Example: The ages of respondents

  14. 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. Working with Quantitative Data Quantitative data can be further described by distinguishing between discrete and continuous types.

  16. Discretedata 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. 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. Nominal- categories only Ordinal- categories with some order Interval- differences but no natural zero point Ratio- differences and a natural zero point Summary - Levels of Measurement

  19. Random Systematic Convenience Stratified Cluster Multistage Methods of Sampling – Summary 1-4

  20. Preview Ch 2 Characteristics of Data 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.

  21. Ch 2-3 Example IQ scores from children with low levels of lead.

  22. 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. Example – Discuss the Shape

  24. Ch 2-4 Pareto Chart A bar graph for qualitative data, with the bars arranged in descending order according to frequencies

  25. 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. Ch 2-4 Frequency Polygon uses line segments connected to points directly above class midpoint values.

  27. Ch 2-4 Important PrinciplesSuggested 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. Descriptive Statistics In this chapter we’ll learn to summarize or describethe 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. 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. Ch 3-3 Sample Standard Deviation Formula

  31. Ch3-3 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. Ch 3-3 Example Use either formula to find the standard deviation of these numbers of chocolate chips: 22, 22, 26, 24

  33. Ch 3-3 Example

  34. 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. Ch 3-3 The Empirical Rule

  36. 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. Sample Population

  37. zScore(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. Measures of Position z Score Population Sample Round z scores to 2 decimal places

  39. 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. Find the 5-number summary. Construct a scale with values that include the minimum and maximum data values. Construct a box (rectangle) extending from Q1 to Q3 and draw a line in the box at the value of Q2 (median). Draw lines extending outward from the box to the minimum and maximum values. Ch3-4 Boxplot - Construction

  41. Ch3-4 Boxplots

  42. An outlier is a value that lies very far away from the vast majority of the other values in a data set. Ch 3-4 Outliers

  43. Ch 3-4Important 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. 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.

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