AP Stats Introduction - Math with Mayer

[Pages:4]INTRODUCTION TO STATISTICS

UNIT 1, LESSON 1; AP STATS

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HIRING DISCRIMINATION

With your neighbors, talk about and complete the distributed activity.

Introduction to AP Stats Hiring discrimination: It just won't fly! An airline has just finished training 25 junior pilots--15 male and 10 female--to become captains. Unfortunately, only eight captain positions are available right now. Airline managers announce that they will use a lottery process to determine which pilots will fill the available positions. The names of all 25 pilots will be written on identical slips of paper, placed in a hat, mixed thoroughly, and drawn out one at a time until all eight captains have been identified. A day later, managers announce the results of the lottery. Of the 8 captains chosen, 5 are female and only 3 are male. Some of the male pilots who were not selected suspect that the lottery was not carried out fairly. One of the pilots knows that you are taking a statistics class, and comes to you for advice. You offer to consult with your classmates and get back to him. The key question in this possible discrimination case seems to be: is it plausible (believable) that these results happened just by chance? To find out, you and your classmates will simulate the lottery process that airline managers said they used. 1. Without looking, remove 8 beads from the bag. Count the number of female pilots selected. Then return the beads to the bag. 2. Your teacher will draw and label axes for a class dotplot. Plot the number of females you obtained in Step 1 on the graph. 3. Repeat Steps 1 and 2 if needed to get a total of at least 40 simulated lottery results for your class.

0 1 2 3 4 5 6 7 8 Number of female pilots chosen in fair lottery

4. Discuss the results with your classmates. Does it seem believable that airline managers carried out a fair lottery? What advice would you give the male pilot who contacted you?

5. Would your advice change if the lottery had chosen 6 female (and 2 male) pilots? What about 7 female pilots? Explain.

STATISTICAL THINKING

The activity models the components of the statistical problem solving process that we will be using throughout this course:

1. Posing a research question ? determining a direction of the research 2. Data Analysis ? breaking down the data gathered 3. Probability Model ? analyzing the likelihood of events occurring based on results,

past and present. 4. Inference ? drawing conclusions go beyond the immediate data.

DEFINITION OF STATISTICS

? Statistics is the science of data, the art of examining data.

What, then, constitutes data? ? A set of data tells information about

individuals. ? Individuals are the objects described by a set

of data, and may be people, animals, or things.

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EX 1: WHAT INDIVIDUALS DO THE DATA DESCRIBE?

EX 2: WHAT INDIVIDUALS DO THE DATA DESCRIBE?

BACK TO INDIVIDUALS...

After it's determined what individuals are being described, the variables then have to be identified.

? A variable is any characteristic of an individual. A variable can take different values for different individuals.

? Further, there are two types of variables.

Categorical

Places an individual into one of several groups or categories

Quantitative

Takes numerical values for which it makes sense to find an average

EX 1: WHAT VARIABLE IS BEING MEASURED? AND WHAT KIND OF VARIABLE IS IT?

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EX 2: WHAT VARIABLES ARE BEING MEASURED? AND WHAT KIND OF VARIABLES ARE THEY?

? Province (Categorical) ? Gender (Cat.) ? Number of languages

spoken (Quantitative) ? Handedness (Cat.) ? Height (Quant.) ? Wrist circumference

(Quant.) ? Preferred

communication method (Cat.) ? Travel time to school (Quant.)

HOW TO EXPLORE DATA

1. Examine each variable by itself. (units 1 & 2) ?This includes investigating the distribution of a variable: the distribution tells us what values the variable takes and how often it takes these values.

2. Move on to study relationships among the variables. (unit 3)

3. Begin with a graph or graphs.

4. Add numerical summaries.

GRAPHICAL DISPLAYS OF DATA: SO MANY CHOICES!

GRAPHING CATEGORICAL DATA

Bar graphs and pie charts both represent the distribution of categorical data.

Pie charts must include all the categories that make up a whole, as the emphasis of each category's relation to the

whole.

Bar graphs are more flexible than

pie charts, showing each category as a bar; bar graphs can compare any set of quantities in the same units.

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HOLD UP...DON'T GET TOO GRAPH CRAZY.

This is a misleading graph. Any ideas why?

By using a pictograph, our eyes are reacting to the adjustment of the proportional shape; instead of focusing on the difference in one dimension (height), we are focusing on the difference in two dimensions (height and width), aka the area of the shapes. The difference is more dramatic than intended.

STILL GETTING CRAZY WITH GRAPHS.

Which one is deceptive, and why? What impression do you get?

The bar graph on the right is misleading, as it doesn't start at 0. This makes the PC ownership look dramatically different, less than half that of the "none" category. The relative frequencies are distorted.

ON YOUR OWN TO SHARE

1. Using our class, identify one group of individuals. 2. From these individuals, identify two variables we could measure, one categorical

and one quantitative. 3. Then, repeat #1 and #2, but with a non-human group of individuals. (*note:

remember, these individuals do NOT have to be physically in the classroom...they can be, but don't get too confined with what I'm asking). Homework: 1, 3, 5, 7, 8, 11, 13, 15, and 17 from section 1.1 of newer edition handout. Also, create the glossary for the terminology from 1.1.

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