Chapter 2 – Study Notes

 

1. Read through the explanations of Describing, Exploring and Comparing data sets (on page 34) until you can explain the differences between the three ideas.
2. What are descriptive statistics used for?
3. What are inferential statistics used for?
4. What are the 5 most important characteristics of data?
5. Why is it important to perform manual calculations before learning to use the calculator or computer software to perform the calculations?
6. What is a frequency table?
7. Study the definitions of lower class limits, upper class limits, class boundaries, class midpoints and class width until you understand these terms and how to calculate them.
8. Study the information on CONSTRUCTING FREQUENCY TABLES (page 36-8)
9. Define relative frequency table and know how to calculate it.
10. Define cumulative frequency table and know how to calculate it.
11. The examples on page 39 are useful – study them until you understand them.

 

Work through the odd numbered exercises on page 40-41 – after you have worked the problems, then check your work with the answers given in the appendix.

 

12. What is the purpose of constructing a graph?
13. What is a histogram?
14. What is the difference between a histogram and a relative frequency histogram? Will they have the same shape?
15. What is a frequency polygon and how is it related to a histogram?
16. What is an ogive?
17. What is a dotplot?
18. Study the example of a stem and leaf plot and the various examples given on page 45
19. What is a Pareto Chart?
20. What is a Pie Chart?
21. Define a scatter diagram?
22. Two classic charts are given on pages 48 and 49 – spend some time with them.
23. What are the factors to be considered when describing data?

 

Answer the odd numbered exercises on page 51-54 – then check your answers with those given in the appendix.

 

24. What are the four measures of the center of a set of data?
25. What is the mean? How is it calculated? What does the Greek letter sigma denote? What is ‘x-bar’?
26. What is the difference between ‘n’ and ‘N’?
27. What is the disadvantage of the mean?
28. Define median. How is it calculated for a set of even values? How is it calculated for a set of odd values? How is it designated?
29. What is the mode? What is bimodal? Multimodal? Does every set of data have a mode? Symbolically, how is the mode designated?
30. What is the midrange? How is it calculated?
31. Study Figure 2-12 until you understand the differences between mode, median, mean and midrange.
32. What is mean by the term ‘average’? From Table 2-11, what are the 4 different values for average for the QWERTY keyboard?
33. What is the rule for rounding numbers?
34. Study the method used to calculate a mean from a frequency table on page 61 until you understand it.
35. Study the calculation of a weighted mean (page 62) – this is a fairly common calculation, so you may already be familiar with it.
36. Study the table on page 63 – read through each column.
37. What is skewness? What is the difference between negatively skewed and positively skewed? (a hint – LMN and PQR – Left skewed is Negative skewed and Positive skewed is Right Skewed – the letters are close to each other in the alphabet)
38. Study the figures at the top of page 64 – memorize the order of the mode, median and mean for each example
39. What is meant by zero skewness?
40. Go through the calculations with STATDISK given on page 64.

 

Work through the odd problems on page 65-68 and then check your answers in the back of the book.

 

41. What are the 4 key concepts about variation which are given on page 68?..
42. What is the range and how is it calculated?
43. What is the standard deviation and how is it calculated? Explicit instructions are given on page 71.
44. What is the mean absolute deviation and how is it calculated?
45. Study the example of calculating the standard deviation on page 72 until you thoroughly understand it.
46. On page 73, there is a self-test suggestion – it would be good to work through the calculations and verify that you can arrive at the correct answer.
47. What is the difference between the standard deviation of a sample and of a population?
48. What is the difference between variance and variation?
49. How is the variance calculated?
50. The method used to calculate the standard deviation from a frequency table is given on page 75 – know how to calculate this value.
51. What does the standard deviation measure?
52. Values close together will yield a ________ standard deviation while values spread apart will yield a __________ standard deviation.
53. What is the ‘range rule of thumb’?
54. The interpretation at the bottom of 77 makes an important point – study the example and think about the interpretation. Two other examples follow (on page 78)
55.  What is the empirical rule? Why is it important that the definition requires that the distribution be ‘bell-shaped’? Is this rule valid if the distribution is skewed?
56. What is Chebychev’s Theorem?

 

Work through the odd problems on page 81 to 84 and then check your answers.

 

57. What is a z score? How is it calculated?
58. What is Michael Jordan’s height z score? What is Rebecca Lobo’s height z score? According to height, which is taller? According to z score, which is taller?
59. The median divides the data set into two equal parts. What measurement divides the data set into 4 equal parts?
60. Is there a universally accepted way to calculate quartiles?
61. What are deciles?
62. How is the percentile calculated?
63. Study the flowchart on page 88 to understand how Percentiles are determined.
64. An important point is made towards the bottom of page 89. What happens to the discrepancy as the sample size increases? Also, the discrepancy can be eliminated by using __________ instead of rounding.
65. Note the calculations of the various types of ranges on the top of page 90.

 

Work through the odd problems on page 91 to 93 and then compare your answers with those in the appendix.

 

66.  What is an outlier? What effects can an outlier have on the exploratory data analysis?

67.  When can outliers be deleted or corrected?

68.  What is a 5-number summary?

69.  What is a boxplot?

70.  Note the tools that have been studied thus far in this course on page 97.

71.  Read through the RAIN example on page 99-101

72.  Work through the STATDISK example on page 101

 

Work through the odd problems on pages 102-103

 

Work through the Review exercises and cumulative review exercises on page 106-7 – check your answers in the back of the book.

 

MATH 1442 students – Answer the 5 questions on page 104 and read through the CRITICAL THINKING project on page 109. Email the answers to the 5 questions and the answers to the following questions to [email protected]. The additional questions are:

a.       Give at least one criticism of the keyboard study that was used throughout this chapter.

b.      Based on your interpretation of the data and the criticism that you listed above, does it appear that the Dvorak keyboard is really more efficient than the QWERTY keyboard?

c.       If someone was just learning to type, which keyboard would you recommend and why?

As you answer these questions, please understand that there may not be a right or wrong answer. Statistics is a study of using the tools available to you and making a decision. The important idea is that you are able to defend your decision or answer based on the tools that you use. It doesn’t mean that others have to agree with you, but they have to have some confidence in the method that you used to arrive at your conclusion. This email must be sent before taking the Chapter 2 test.

 

The Chapter 2 test will be available starting on _______ until _____. It consists of 20 questions and has a time limit of 40 minutes. You can use your textbook and notes as you take the test.