TL-2-1

The future belongs to those who believe

in the beauty of their dreams.

- Eleanor Roosevelt

Overview of Investigation 2Goals:

to note the kind of data being collected; that is, categorical or numerical

to use bar graphs to display categorical and numerical data

to understand how measures of center (median, mode) and spread (range) relate to numerical and categorical data

Investigation 2: Types of Data

Materials (p. 21l)

Student Handbook Pages (pp. 22 - 29)

Teaching the Investigation (pp. 29a – 29d)TI-2-2

Types of Data

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Some questions have answers that are words or categories, and other questions

have answers that are numbers.

In what month were you born?

What kinds of pets do you have?

How many pets do you have?

Who is your favorite author?

How much time do you spend watching televison in a day?

What is your highest score in the game Yahtzee?

What color are your eyes?

How many movies have you watched in the last week?

How do you get to school?

Investigation 2.1

Categorical Data -data that are words or categories.

Numerical Data- data that are numbers

Problem 2.1

Think of some things you would like to know more about. Then, develop questions you could ask to gather information about those things.

A. Write two questions that have categorical data as answers.

B. Write two questions that have numerical data as answers.

The pets people have often depend on where they live. People who live in cities have small pets, while people who live on farms often have large pets. People who live in apartments are sometimes not permitted to have

pets at all.

Counting Pets 2.2

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The two questions that each student asked were:

What is your favorite kind of pet? How many pets do you have?

Counting Pets

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Problem 2.2

Decide whether each question below can be answered by using data from the graphs the students created. If a question can be answered, give the answer and explain how you got it. If a question cannot be answered, explain why not and tell what additional information you would need to answer the questions.

Problem 2.2

A. Which graph shows categorical data, and which graph shows numerical data?

B. What is the total number of pets the students have?C. What is the greatest number of pets that any student in

the class has?D. How many students are in the class?E. How many students chose cats as their favorite kind of

pet?F. How many cats do students have as pets?G. What is the mode for the favorite kind of pet?H. What is the median of the numbers of pets students have?I. What is the range of the numbers of pets students have?J. Thomas is a student in this class. How many pets does he

have?K. Do the girls have more pets than the boys?

Problem 2.2 follow-up

Do you think the students surveyed live in the city, the suburbs, or the country? Explain your answer.

Works of the Heart

Blessed is the man whose Dream outlives him.

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Investigation 3

Using Graphs to Group your Data

Goals:to use stem-and-leaf plots to group numerical data in intervals

to use the ordered data in a stem plot to locate measures of center (median and mode) and measure of spread (range)

to describe the shape of the data, including the location of clusters and gaps, and to determine what is typical about the data

to compare two data sets by using back-to-back stem-and-leaf plots

to compare two data sets by using statistics, such as median and range

Investigation 3: Using Graphs to Group DataMaterials (p. 29f)

Student Handbook Pages (pp. 30 - 41)

Teaching the Investigation (pp. 41a – 41h)

Overview of Investigation 3

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What three questions did the students ask?

How might the students have collected the data to answer these questions?

Would a line plot be a good way to show the travel-time data? Why or why not?

Traveling to School

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Look at the table of data and the labels for the columns, and consider these questions:

A stem-and-leaf plot looks something like a stem with leaves.

Making a Stem-and-Leaf Plot

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Stem Leaves

The other digits in the data

values form the stem.

The “leaves” are the units digits of the data values.

We show the tens digits as a “stem” of numbers:

Making a Stem-and-Leaf Plot

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Stem

Tens Digits

We show the ones digit as a “leaf” next to its tens digits:

Making a Stem-and-Leaf Plot

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Leaves

Ones Digits

Can you figure out how these data were added as leaves to the stem plot?

Making a Stem-and-Leaf Plot

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Ones Digits

Leaves

Notice that the leaves are not in ascending order; they are recorded as they occur in the data list.

Making a Stem-and-Leaf Plot

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Notice that the leaves are rearranged in order.

Making a Stem-and-Leaf Plot

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Problem 3.1

After you have completed your stem plot of the data answer these questions.

A. Which students probably get to sleep the latest in the morning? Why do you think this?

B. Which students probably get the earliest? Why do you think this?

C. What is the typical time it takes students to travel to school?

Problem 3.1 Follow-up

What is the typical time it takes for a student in your class to travel to school?

1. Decide what data you need to collect to answer this question. Then, with your group gather the appropriate data.

2. Find a way to organize an display your data.

3. After looking at your data, what would you say is the typical time it takes for a student in your class to travel to school?

Jumping Rope 3.2

Which class did better overall in the jump-rope activity? Use what you know about statistics to help you justify your answer.

3.2 Follow-up- Vocabulary

In Mr. Koick’s class, there are some very large numbers of jumps. For example, one student jumped 151 times, and another student jumped 300 times. We call these data outliers.

Outliers are values that stand out in a set of data.

3.2 Follow-up

1. Find two other out liers in the data for Mr. Kocik’s class.Statisticians question outliers and try to figure out why they might have occured. An outlier may be a value that was recorded incorrectly, or it may be a signal that something special is happening that you may want to understand.2. All the values recorded for Mr. Kocik’s class are correct. What do you think might account for the few students who were able to jump many more times that their classmates?In 3-5, use the data you collected in Problem 3.1 Follow-up about the time it takes for you and your classmates to travel to school.3. Make a back-to back- stem plot showing your class data and the data form the Wisconsin class that was used in Problem 3.1.4. How do your data and the Wisconsin data compare?5. Are there any outliers in either of the two data sets? Explain.

TL-3-1

A great deal of good can be done in the world if one is not too concerned with who gets the credit.

- Jesuit motto