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Chapter 1: Introduction to Statistics Blackboard / CourseCompass / Web CT Demo |
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Look at pages 30 and 31 in your textbook. The purpose of this chapter is to introduce the standard tools of descriptive statistics that professionals use to summarize data such as those describing the ages of residents in Akhiok, Alaska. As a working professional, you will surely be using data to project budgets, forecast financial trends, or understand marketing efforts. You will be expected to use and understand the statistical tools described in this chapter.
Chapter 2.1
Chapter 2.2
Chapter 2.3
Chapter 2.4
Chapter 2.5
What is most important:
Organizing quantitative data into readable classes, with a consistent width.
Constructing a frequency distribution to visualize patterns.
Drawing a frequency histogram to present trends in your data.
Understanding relative frequency as a prelude to probability.
Reading 
Read page 32. Often we start with our class width, rather than the number of classes to make our displays readable. (Classes like 0-9, 10-19, 20-29, ... or classes like $0-$999, $1000-$1999, $2000-$2999 are preferable to start with because of their readability.) When you plan a presentation, you want your graphics to be readable to your audience.
Read page 33. Note the study tip about the greek letter sigma used to indicate a sum. Notice how it is used in the table on page 33.
Read about midpoints and relative frequency on pages 34 and 35.
A frequency histogram is the most commonly used statistical graph of a frequency distribution. Read how to construct one on page 36. Look at the relationships between the midpoint and frequency on the table on page 35 and the horizontal and vertical axes on the graph on page 36. Notice on the histogram that the bars touch and that the horizontal axis and the vertical axis are consistently scaled as a number line like the graphs in your other mathematics classes.
Frequency polygons contain the same information as a histogram or a frequency table. Read page 37 including the study tip. Newspaper graphs often use frequency polygons. Look in the business section of your local newspaper the next time you get a chance. Skim the rest of this section.
Exercises 
1, 3, 5, 7, 11, 13, 15, 19, 23, 29
Chapter 2.2 - More Graphs and Displays
What is most important:
How to construct a stem-and-leaf plot.
Brief introduction to other commonly used graphs: scatter plots, time series, pie charts, and Pareto charts.
Reading
Read pages 46 and 47. Stem-and-leaf plots are another way professionals display data. Stem-and-leaf plots are sometimes preferred for small sets of data, when it is useful to see the original values, rather than combining values into classes. Stem-and-leaf plots are not preferable for large sets of data. Histograms can better handle large collections of data, but some detail is lost when data values are tallied into classes.
Lightly read pages 48 through 52. Scatter plots and time series will be considered later in Chapter 9.
Exercises
1, 3, 7, 15, 17
Suggested Practice 
Open Statlet Chapter 2-single data column. Enter the ages of residents of Akhiok, Alaska, found on page 31 or click on Example. (See the note below). Create the histogram on page 31 by clicking on Histogram. (Click on Options if you want to control class width and number of classes for your histogram). Create a stem-and-leaf plot of these data (click on Stem-leaf). Which type of graph do you prefer for reading these data? Why?
Note: We will use these data again for Chapter 2.4 and Chapter 2.5. You may avoid entering data multiple times if you enter the ages into a file on your personal computer (click on Clipboard and then click on help for detailed instructions using Clipboard). Try this before you move on.
Chapter 2.3 - Measures of Central Tendency
What is most important:
Understanding how to calculate the mean of quantitative data.
Calculating a weighted mean.
Estimating the mean of data already tabulated into classes.
Understanding when the median may be a more appropriate measure of center than the mean.
Reading
Read about the mean, median, and mode on pages 57 through 60. Notice in Example 6 the discussion of outliers and where a median can be a better measure of center.
Example: If you finished the following courses this semester, would you know how to calculate your GPA for the semester? (Note: It isn't (4.0+3.0+2.0+3.0) / 4 = 3.0.) Do you know why?
| Course | Credits | Grade |
| Mathematics | 3 | 4.0 |
| Economics | 4 | 3.0 |
| Biology | 5 | 2.0 |
| English | 3 | 3.0 |
Read about weighed means and the mean of a frequency distribution on pages 61-62.
Lightly read about symmetry and when a distribution is skewed on page 63.
Example continued: To calculate your GPA you would sum total points and divide by the total number of credits. GPA = 43 / 15 = 2.87
| Course | Credits | Grade | Points |
| Mathematics | 3 | 4.0 | 3*4.0 = 12 |
| Economics | 4 | 3.0 | 4*3.0 = 12 |
| Biology | 5 | 2.0 | 5*2.0 = 10 |
| English | 3 | 3.0 | 3*3.0 = 9 |
| TOTAL | 15 | 43 |
Exercises 
1, 3, 13, 21, 23, 25, 29, 31, 33, 35, 37
Chapter 2.4 - Measures of Variation
What is most important:
Calculating the range and standard deviation of quantitative data.
Being able to explain the meaning of standard deviation in the context of a particular application.
Understanding the simple relationship between standard deviation and variance.
Reading
Most beginning statistics students think that knowing the range and mean of a set of data is enough.
Example: How would you compare two small classes of math students with the same mean and range on a first quiz worth 50 points?
Scores - 1'st Class
50
30
30
30
30
30
30
30
30
10
Scores - 2'nd Class
50
50
50
50
50
10
10
10
10
10
Are these two classes different? Both have the same mean of 30, both have the same maximum of 50, and both have the same minimum 10.
The difference you see between these two classes is described with a number called standard deviation. Lightly read pages 71-72. Complete Try It Yourself 3 (using data on page 70).
Standard deviation tells you how far most values in your data deviate from the mean. If you consider the value calculated for Corporation A on page 72, what it means is that most of the starting salaries were within 2.97 (about 3) of the mean 41.5. Look at the list of salaries - are most of them between 41.5 + 3, and 41.5 - 3, between 38.5 and 44.5?
Example continued: Look agin at the two classes of quiz scores discussed above.
Scores - 1'st Class
50
30
30
30
30
30
30
30
30
10
Scores - 2'nd Class
50
50
50
50
50
10
10
10
10
10
Think about how you would compare the standard deviation for these two clases. Are they the same? Is the standard deviation for the first class larger? The answer to both of those questions is no. Since the first class has more scores which are closely clustered in the middle, closer to the mean, the standard deviation for the first class will be smaller.
Understanding standard deviation is an important part of using descriptive statistics. Calculating the value can be simplified using technology. Page 74 and the Suggested Practice below address using software to calculate standard deviation.
Read Example 6 to help you understand the number you calculate for standard deviation.
Read about bell-shaped distributions on page 76.
Exercises
1, 3, 13, 15, 17 (use technology), 19 (use technology), 21
Suggested Practice
Open Statlet Chapter 2-single data column. (You used this earlier in section 2.2.) Enter the salaries for Corporation A from Example 3. Click on Stats. Notice the value for standard deviation 3.1358 does not match the hand calculations from the textbook. This statlet gives the sample standard deviation, s. The book is calculating the population standard deviation. This Statlet could save you time as you complete exercises 17 and 19.
Chapter 2.5 - Measures of Position
What is most important:
Describing the relative position of an individual within the group using the individual's percentile and the individual's Z-score.
Understanding quartiles.
Reading and understanding box-and-whisker plots.
Reading
Read page 87 about quartiles and complete Try It Yourself 1. Lightly read page 88, focusing on the technology you are using. (Note: Statlet Chapter 2-single data column will give you this same information.)
Read the study tip on page 88. Do not worry if your calculation is off by one data entry in the ordered list of data. For example for the data on page 88, if you used the sixth entry in order, which is 21 for Q1, or the seventh entry, 22, or their mean, 21.5, any one of those would be considered correct.
Read pages 89 and 90 focusing on Example 4. Complete Try It Yourself 4 for practice. Look at Picturing the World on page 90 and answer their question at the end. (The IQR represents the middle 50 percent. Roughly 22 of the U.S. presidents have been between 51 and 58 years old.)
Read page 91. Notice how the percentile of an individual's score describes what percentage of the group scored below the individual. Complete Try It yourself 5.
Z-scores will be the way we measure the position of an individual most often. Carefully read page 92 making sure you understand all details, especially the interpretation. Carefully complete Try It Yourself 6.
An individual's z-score tells us how many standard deviations the individual falls from the mean.
Z-scores will give us extremely important information when we study bell-shaped distributions and make statistical inferences in later chapters.
Exercises
1, 5, 7, 11, 15, 21, 23, 31
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