## Unit 1 Activities

##### Time Advisory

Completing this unit should take approximately 5 hours and 30 minutes.

- Subunit 1.1: 50 minutes
- Subunit 1.2: 35 minutes
- Subunit 1.3: 1 hour and 30 minutes
- Subunit 1.4: 2 hours and 35 minutes

##### Learning Outcomes

Upon successful completion of this unit, you will be able to:

- Distinguish between quantitative and categorical variables.
- Describe the difference between a population and a sample and be able to distinguish between a parameter and a statistic.
- Given a type of measurement, identify the correct level of measurement: nominal, ordinal, interval, or ratio.
- Calculate the mean, median, and mode for a set of data, and compare and contrast these measures of center.
- Identify the symbols and know the formulas for sample and population means.
- Calculate the midrange, weighted mean, percentiles, and quartiles for a data set.
- Calculate the range, the interquartile range, the standard deviation, and the variance for a population and a sample, and know the symbols, formulas, and uses of these measures of spread.

##### Standards Addressed (Common Core and AP):

- CCSS.Math.Content.HSS-ID.A.2
- CCSS.ELA-Literacy.RST.11-12.4
- CCSS.ELA-Literacy.RST.11-12.5
- CCSS.ELA-Literacy.RST.11-12.7
- CCSS.ELA-Literacy.RST.11-12.10
- AP I.B.1
- AP I.B.2
- AP I.B.3

**1.1 Statistical Terminology**

*The intent of this first section of the first unit is to introduce you to the terminology of statistics. Please make note of the following: quantitative variable, categorical variable, sample, population, statistic, and parameter. These terms will be used frequently throughout the course.*

**Explanation:** Saylor Academy's Flexbook: Jill Schmidlkofer's *Advanced Probability and Statistics*: "Section 1.1: Statistical Terminology”; partially adapted from David Lane's *Online Statistics Education: An Interactive Multimedia Course of Study* and CK-12: *Advanced Probability and Statistics* (PDF)

Instructions: Click on the link above and read Section 1.1. Statistics has its own language, and getting a foundation in the course requires that you become fluent with the basic vocabulary. Take notes about the new statistics terms that you learn as you read about Galapagos tortoise reintroduction.

Reading this section and taking notes should take approximately 30 minutes.

*Standards Addressed (Common Core and AP):*

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is adapted from works attributed to David Lane and CK-12, which can be found here and here.

**Checkpoint**: Saylor Academy's Flexbook: Jill Schmidlkofer's *Advanced Probability and Statistics*: "Section 1.1: Statistical Terminology”; partially adapted from David Lane's *Online Statistics Education: A Multimedia Course of Study* and CK-12: *Advanced Probability and Statistics* (PDF)

Instructions: Answer the review questions at the end of Section 1.1. You will use the vocabulary words learned in the section to answer them. A short answer key is provided at the end of the problem set.

Completing the review questions should take approximately 20 minutes.

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is adapted from works attributed to David Lane and CK-12, which can be found here and here.

**1.2 An Overview of Data**

*The way we collect, display, and analyze data depends on the type of data in which we are interested. Therefore, we learn in this subunit more vocabulary about the four main types of data: nominal, ordinal, interval, and ratio.*

**Explanation**: Saylor Academy's Flexbook: Jill Schmidlkofer's *Advanced Probability and Statistics*: "Section 1.2: An Overview of Data”; partially adapted from David Lane's *Online Statistics Education: A Multimedia Course of Study* and CK-12: *Advanced Probability and Statistics* (PDF)

Instructions: Read Section 1.2. In statistics, we analyze and interpret different types of data. For example, exam grades of A, B, C, D, and F are different from exam scores of 92, 85, 76, 61, and 45. Each type is valid, but we analyze the types differently. Therefore, a good foundation of the types of data available and their classifications is important.

Reading this section and taking notes should take approximately 25 minutes.

*Standards Addressed (Common Core and AP):*

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is adapted from works attributed to David Lane and CK-12, which can be found here and here.

**Checkpoint**: Saylor Academy's Flexbook: Jill Schmidlkofer's *Advanced Probability and Statistics*: "Section 1.2: An Overview of Data”; partially adapted from David Lane's *Online Statistics Education: A Multimedia Course of Study* and CK-12: *Advanced Probability and Statistics* (PDF)

Instructions: Answer the review questions at the end of Section 1.2. You will identify the level of data that is described in several scenarios. A short answer key is provided at the end of the problem set.

Completing the review questions should take approximately 10 minutes.

**1.3 Measures of Center**

*A set of raw data is just a bunch of numbers. We learn to organize and summarize the raw data in this subunit by calculating the familiar mean, median, mode, and weighted mean. But we also learn to group the raw data into quartiles and percentiles. Pay close attention to the symbols and formulas in this subunit. You will see them again!*

**Explanation**: Saylor Academy's Flexbook: Jill Schmidlkofer's *Advanced Probability and Statistics*: "Section 1.3: Measures of Center”; partially adapted from David Lane's *Online Statistics Education: A Multimedia Course of Study* and CK-12: *Advanced Probability and Statistics* (PDF)

Instructions: Read Section 1.3. Take notes and work the examples provided as you read. Detailed instructions for using the TI-83/84 calculator are provided.

Reading this Section, taking notes, and working through the examples should take approximately 40 minutes.

*Standards Addressed (Common Core and AP):*

- CCSS.Math.Content.HSS-ID.A.2
- CCSS.ELA-Literacy.RST.11-12.4
- AP I.B.1
- AP I.B.3

**Web Media**: Khan Academy's "Statistics Intro: Mean, Median and Mode” (YouTube)

Instructions: Click on the link above and take notes as you watch the video. This is an easy topic. You should mentally work ahead of the instructor, anticipating his next step.

Watching this lecture and taking notes should take approximately 10 minutes.

*Standards Addressed (Common Core and AP):*

- CCSS.Math.Content.HSS-ID.A.2
- AP I.B.1

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to Khan Academy.

**Activity**: Shodor: "Plop It! An Interactive Study of the Mean and the Median”

Instructions: Begin this exercise by entering six data values into the box on the right (Example: 3, 3, 4, 4, 5, 6). A histogram of the data will appear. Look below the histogram and note the values of the mean and the median. Now, click on the "drag block” radio button, and click on the "6” box, moving it up to the value 14. What has happened to the median? What has happened to the mean? When you moved the box to the value 14, you created an outlier, and the median didn't change, but the mean did. This property of the median is called resistance. The median is resistant to the effects of an outlier, but the mean is not resistant, because its value is affected by an outlier.

Now, spend some time playing with the data and the histogram. See what happens if you pile all the boxes on top of each other. Enter a new set of data values, half of which are very small and half of which are very large. Then move the boxes around, seeing what happens to the mean and the median after each move.

Completing this activity should take approximately 10 minutes.

*Standards Addressed (Common Core and AP):*

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

**Checkpoint**: Saylor Academy's Flexbook: Jill Schmidlkofer's *Advanced Probability and Statistics*: "Section 1.3: Measures of Center”; partially adapted from David Lane's *Online Statistics Education: A Multimedia Course of Study* and CK-12: *Advanced Probability and Statistics* (PDF)

Instructions: Answer the review questions at the end of Section 1.3. Use your calculator to perform some of the statistical calculations. A short answer key is provided at the end of the problem set. For a detailed solution, click here.

Completing the review questions should take approximately 30 minutes.

*Standards Addressed (Common Core and AP):*

- CCSS.Math.Content.HSS-ID.A.2
- AP I.B.1
- AP I.B.3

**1.4 Measures of Spread**

*Assume that two cities have an average year-round temperature of 76 degrees. You want to go sightseeing in February, and you think that either city would be a good choice. Hold on! What if City A has a temperature of 76 degrees every day, whereas City B has summer temperatures of 100+ degrees and winter days as cold as 10 degrees below zero? Both can boast the same average temperature, but we also have to consider how far from the average the really cold or really hot days vary. That is what we call the spread of the data, and that is the subject of this subunit. Pay close attention to the standard deviation and the interquartile range, both of which will be used in later units in this course.*

**Explanation:** Saylor Academy's Flexbook: Jill Schmidlkofer's *Advanced Probability and Statistics*: "Section 1.4: Measures of Spread”; partially adapted from David Lane's *Online Statistics Education: A Multimedia Course of Study* and CK-12: *Advanced Probability and Statistics* (PDF)

Instructions: Read Section 1.4. Take notes, and work the examples as you read. You will be given additional instructions for calculating the standard deviation and interquartile range with the TI-83/84 calculator.

Reading this section, taking notes, and practicing new calculator skills should take approximately 90 minutes.

*Standards Addressed (Common Core and AP):*

- CCSS.Math.Content.HSS-ID.A.2
- CCSS.ELA-Literacy.RST.11-12.4
- AP I.B.1
- AP I.B.2
- AP I.B.3

**Web Media:** Khan Academy's "Variance of a Population” (YouTube)

Instructions: Click on the link above and take notes as you watch the video. This is an introduction to the variance of a population. Pay attention to the concept, and note the relationship between the variance and the standard deviation.

Watching this lecture and taking notes should take approximately 10 minutes.

*Standards Addressed (Common Core and AP):*

- CCSS.Math.Content.HSS-ID.A.2
- AP I.B.2

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to Khan Academy.

**Web Media**: Khan Academy's "Sample Variance” (YouTube)

Instructions: Click on the link above and take notes as you watch the video. This is an introduction to the variance of a sample. Pay attention to the concept, and note the relationship between the variance and the standard deviation. The standard deviation will be used throughout the second half of the course, so it will be to your benefit to master its definition, uses, symbol, and calculation.

Watching this lecture and taking notes should take approximately 15 minutes.

*Standards Addressed (Common Core and AP):*

- CCSS.Math.Content.HSS-ID.A.2
- AP I.B.2

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to Khan Academy.

**Checkpoint**: Saylor Academy's Flexbook: Jill Schmidlkofer's *Advanced Probability and Statistics*: "Section 1.4: Measures of Spread”; partially adapted from David Lane's *Online Statistics Education: A Multimedia Course of Study* and CK-12: *Advanced Probability and Statistics* (PDF)

Instructions: Answer the review questions at the end of Section 1.4. Use your calculator where appropriate for assistance in answering the questions. A short answer key is provided at the end of the problem set. For a detailed solution, click here.

Completing the review questions should take approximately 40 minutes.

*Standards Addressed (Common Core and AP):*

- CCSS.Math.Content.HSS-ID.A.2
- AP I.B.1
- AP I.B.2
- AP I.B.3