MATH 105: Finite Mathematics 9-1: Introduction to Statistics Prof. - - PowerPoint PPT Presentation

Vocabulary Types of Data Samples Conclusion

MATH 105: Finite Mathematics 9-1: Introduction to Statistics

• Prof. Jonathan Duncan

Walla Walla College

Winter Quarter, 2006

Vocabulary Types of Data Samples Conclusion

Outline

1

Vocabulary

2

Types of Data

3

Samples

4

Conclusion

Vocabulary Types of Data Samples Conclusion

Outline

1

Vocabulary

2

Types of Data

3

Samples

4

Conclusion

Vocabulary Types of Data Samples Conclusion

Statistics vs. Probability

We just several chapters on probability. Probability involves taking a general rule and using it to make guesses about the outcome of a specific event. Example Using probability rules you determine that the expected value of rolling a single die is 3.5 (1

6(1) + 1 6(2) + . . . + 1 6(6))

Example You roll the die 100 times and take the average of the rolls to determine what the typical roll of the die will be.

Vocabulary Types of Data Samples Conclusion

Statistics vs. Probability

We just several chapters on probability. Probability involves taking a general rule and using it to make guesses about the outcome of a specific event. Example Using probability rules you determine that the expected value of rolling a single die is 3.5 (1

6(1) + 1 6(2) + . . . + 1 6(6))

Example You roll the die 100 times and take the average of the rolls to determine what the typical roll of the die will be.

Vocabulary Types of Data Samples Conclusion

Statistics vs. Probability

We just several chapters on probability. Probability involves taking a general rule and using it to make guesses about the outcome of a specific event. Example Using probability rules you determine that the expected value of rolling a single die is 3.5 (1

6(1) + 1 6(2) + . . . + 1 6(6))

In this chapter we look at statistics which work in reverse. We take specific sets of data and try to generalize what we find to the entire Example You roll the die 100 times and take the average of the rolls to determine what the typical roll of the die will be.

Vocabulary Types of Data Samples Conclusion

Statistics vs. Probability

We just several chapters on probability. Probability involves taking a general rule and using it to make guesses about the outcome of a specific event. Example Using probability rules you determine that the expected value of rolling a single die is 3.5 (1

6(1) + 1 6(2) + . . . + 1 6(6))

In this chapter we look at statistics which work in reverse. We take specific sets of data and try to generalize what we find to the entire Example You roll the die 100 times and take the average of the rolls to determine what the typical roll of the die will be.

Vocabulary Types of Data Samples Conclusion

Statistical Process

The Statistical Process The statistical process involves the following steps.

1 Collecting data from a sample of individuals in a population. 2 Analyzing that data by graphing, finding measures of

center and spread, and more.

3 Making inferences from the data.

Example To determine the P:resident’s approval rating a polling company:

1 calls a chosen group of voters. 2 compiles the data to determine what percent approve. 3 infers that the country in general has the same opinion as

those sampled with an error of ±x%.

Vocabulary Types of Data Samples Conclusion

Statistical Process

The Statistical Process The statistical process involves the following steps.

1 Collecting data from a sample of individuals in a population. 2 Analyzing that data by graphing, finding measures of

center and spread, and more.

3 Making inferences from the data.

Example To determine the P:resident’s approval rating a polling company:

1 calls a chosen group of voters. 2 compiles the data to determine what percent approve. 3 infers that the country in general has the same opinion as

those sampled with an error of ±x%.

Vocabulary Types of Data Samples Conclusion

Statistical Process

The Statistical Process The statistical process involves the following steps.

1 Collecting data from a sample of individuals in a population. 2 Analyzing that data by graphing, finding measures of

center and spread, and more.

3 Making inferences from the data.

Example To determine the P:resident’s approval rating a polling company:

1 calls a chosen group of voters. 2 compiles the data to determine what percent approve. 3 infers that the country in general has the same opinion as

those sampled with an error of ±x%.

Vocabulary Types of Data Samples Conclusion

Statistical Process

The Statistical Process The statistical process involves the following steps.

1 Collecting data from a sample of individuals in a population. 2 Analyzing that data by graphing, finding measures of

center and spread, and more.

3 Making inferences from the data.

Example To determine the P:resident’s approval rating a polling company:

1 calls a chosen group of voters. 2 compiles the data to determine what percent approve. 3 infers that the country in general has the same opinion as

those sampled with an error of ±x%.

Vocabulary Types of Data Samples Conclusion

Statistical Process

The Statistical Process The statistical process involves the following steps.

1 Collecting data from a sample of individuals in a population. 2 Analyzing that data by graphing, finding measures of

center and spread, and more.

3 Making inferences from the data.

Example To determine the P:resident’s approval rating a polling company:

1 calls a chosen group of voters. 2 compiles the data to determine what percent approve. 3 infers that the country in general has the same opinion as

those sampled with an error of ±x%.

Vocabulary Types of Data Samples Conclusion

Statistical Process

The Statistical Process The statistical process involves the following steps.

1 Collecting data from a sample of individuals in a population. 2 Analyzing that data by graphing, finding measures of

center and spread, and more.

3 Making inferences from the data.

Example To determine the P:resident’s approval rating a polling company:

1 calls a chosen group of voters. 2 compiles the data to determine what percent approve. 3 infers that the country in general has the same opinion as

those sampled with an error of ±x%.

Vocabulary Types of Data Samples Conclusion

Statistical Process

The Statistical Process The statistical process involves the following steps.

1 Collecting data from a sample of individuals in a population. 2 Analyzing that data by graphing, finding measures of

center and spread, and more.

3 Making inferences from the data.

Example To determine the P:resident’s approval rating a polling company:

1 calls a chosen group of voters. 2 compiles the data to determine what percent approve. 3 infers that the country in general has the same opinion as

those sampled with an error of ±x%.

Vocabulary Types of Data Samples Conclusion

Statistical Process

The Statistical Process The statistical process involves the following steps.

1 Collecting data from a sample of individuals in a population. 2 Analyzing that data by graphing, finding measures of

center and spread, and more.

3 Making inferences from the data.

Example To determine the P:resident’s approval rating a polling company:

1 calls a chosen group of voters. 2 compiles the data to determine what percent approve. 3 infers that the country in general has the same opinion as

those sampled with an error of ±x%.

Vocabulary Types of Data Samples Conclusion

Outline

1

Vocabulary

2

Types of Data

3

Samples

4

Conclusion

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms 2 Height of a MATH 105 student 3 Number of cars crossing an intersection in an hour 4 How long Junior class members can hold their breath

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms 2 Height of a MATH 105 student 3 Number of cars crossing an intersection in an hour 4 How long Junior class members can hold their breath

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms 2 Height of a MATH 105 student 3 Number of cars crossing an intersection in an hour 4 How long Junior class members can hold their breath

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms (D) 2 Height of a MATH 105 student 3 Number of cars crossing an intersection in an hour 4 How long Junior class members can hold their breath

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms (D) 2 Height of a MATH 105 student 3 Number of cars crossing an intersection in an hour 4 How long Junior class members can hold their breath

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms (D) 2 Height of a MATH 105 student (C) 3 Number of cars crossing an intersection in an hour 4 How long Junior class members can hold their breath

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms (D) 2 Height of a MATH 105 student (C) 3 Number of cars crossing an intersection in an hour 4 How long Junior class members can hold their breath

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms (D) 2 Height of a MATH 105 student (C) 3 Number of cars crossing an intersection in an hour (D) 4 How long Junior class members can hold their breath

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms (D) 2 Height of a MATH 105 student (C) 3 Number of cars crossing an intersection in an hour (D) 4 How long Junior class members can hold their breath

Vocabulary Types of Data Samples Conclusion

So What do we Study?

Vocabulary data information about a particular characteristic of a population. variable a measurable characteristic which can be: discrete – space between values continuous – can assume any value Example Mark each variable Discrete or Continuous.

1 Number of “green clovers” in a box of Lucky Charms (D) 2 Height of a MATH 105 student (C) 3 Number of cars crossing an intersection in an hour (D) 4 How long Junior class members can hold their breath (C)

Vocabulary Types of Data Samples Conclusion

Outline

1

Vocabulary

2

Types of Data

3

Samples

4

Conclusion

Vocabulary Types of Data Samples Conclusion

Collecting Data

The way in which we collect data is very important to the statistical process. Example To measure the height of MATH 105 students, we bring a tape measure to class and record the height of everybody in the class. This gives us the height of the entire population of MATH 105 students. Example To measure the number of “green clovers” in a box of Lucky Charms, we can not check every box. So we check a small number

• f boxes or a sample of the population.

Vocabulary Types of Data Samples Conclusion

Collecting Data

The way in which we collect data is very important to the statistical process. Example To measure the height of MATH 105 students, we bring a tape measure to class and record the height of everybody in the class. This gives us the height of the entire population of MATH 105 students. Example To measure the number of “green clovers” in a box of Lucky Charms, we can not check every box. So we check a small number

• f boxes or a sample of the population.

Vocabulary Types of Data Samples Conclusion

Collecting Data

The way in which we collect data is very important to the statistical process. Example To measure the height of MATH 105 students, we bring a tape measure to class and record the height of everybody in the class. This gives us the height of the entire population of MATH 105 students. It is not always feasible to measure every data point in a population. Example To measure the number of “green clovers” in a box of Lucky Charms, we can not check every box. So we check a small number

• f boxes or a sample of the population.

Vocabulary Types of Data Samples Conclusion

Collecting Data

The way in which we collect data is very important to the statistical process. Example To measure the height of MATH 105 students, we bring a tape measure to class and record the height of everybody in the class. This gives us the height of the entire population of MATH 105 students. It is not always feasible to measure every data point in a population. Example To measure the number of “green clovers” in a box of Lucky Charms, we can not check every box. So we check a small number

• f boxes or a sample of the population.

Vocabulary Types of Data Samples Conclusion

Collecting Data

The way in which we collect data is very important to the statistical process. Example To measure the height of MATH 105 students, we bring a tape measure to class and record the height of everybody in the class. This gives us the height of the entire population of MATH 105 students. It is not always feasible to measure every data point in a population. Example To measure the number of “green clovers” in a box of Lucky Charms, we can not check every box. So we check a small number

• f boxes or a sample of the population.

It is important that we sample boxes which are representative of the entire population of Lucky Charms boxes.

Vocabulary Types of Data Samples Conclusion

Simple Random Sample

Simple Random Sample In a simple random sample, each member of the population being studied has an equally likely chance of being chosen for the sample. Example You survey people in Walla Walla county by assigning a number to each person in the county phone book. You then select 100 of those numbers. Is this a simple random sample?

Vocabulary Types of Data Samples Conclusion

Simple Random Sample

Simple Random Sample In a simple random sample, each member of the population being studied has an equally likely chance of being chosen for the sample. Example You survey people in Walla Walla county by assigning a number to each person in the county phone book. You then select 100 of those numbers. Is this a simple random sample?

Vocabulary Types of Data Samples Conclusion

Simple Random Sample

Simple Random Sample In a simple random sample, each member of the population being studied has an equally likely chance of being chosen for the sample. Example You survey people in Walla Walla county by assigning a number to each person in the county phone book. You then select 100 of those numbers. Is this a simple random sample? Possible sources of bias:

1 People who work not included 2 People with unlisted numbers not included 3 People without phones not included

Vocabulary Types of Data Samples Conclusion

Simple Random Sample

Simple Random Sample In a simple random sample, each member of the population being studied has an equally likely chance of being chosen for the sample. Example You survey people in Walla Walla county by assigning a number to each person in the county phone book. You then select 100 of those numbers. Is this a simple random sample? Possible sources of bias:

1 People who work not included 2 People with unlisted numbers not included 3 People without phones not included

Vocabulary Types of Data Samples Conclusion

Simple Random Sample

Simple Random Sample In a simple random sample, each member of the population being studied has an equally likely chance of being chosen for the sample. Example You survey people in Walla Walla county by assigning a number to each person in the county phone book. You then select 100 of those numbers. Is this a simple random sample? Possible sources of bias:

1 People who work not included 2 People with unlisted numbers not included 3 People without phones not included

Vocabulary Types of Data Samples Conclusion

Simple Random Sample

Simple Random Sample In a simple random sample, each member of the population being studied has an equally likely chance of being chosen for the sample. Example You survey people in Walla Walla county by assigning a number to each person in the county phone book. You then select 100 of those numbers. Is this a simple random sample? Possible sources of bias:

1 People who work not included 2 People with unlisted numbers not included 3 People without phones not included

Vocabulary Types of Data Samples Conclusion

Hinge Quality

Example To determine the quality of hinges produced at the Acme Hinge Factory, ten hinges are randomly selected from the hinges produced in a given day. These ten hinges are then subjected to rigorous endurance testing. Is this a simple random sample? Example You stand outside the cafeteria between 5:30 and 6:30 p.m. on Thursday evening and ask every 5th person if they enjoyed the

• food. Is this a simple random sample of all WWC students? Of all

dorm students?

Vocabulary Types of Data Samples Conclusion

Hinge Quality

Example To determine the quality of hinges produced at the Acme Hinge Factory, ten hinges are randomly selected from the hinges produced in a given day. These ten hinges are then subjected to rigorous endurance testing. Is this a simple random sample? Example You stand outside the cafeteria between 5:30 and 6:30 p.m. on Thursday evening and ask every 5th person if they enjoyed the

• food. Is this a simple random sample of all WWC students? Of all

dorm students?

Vocabulary Types of Data Samples Conclusion

Outline

1

Vocabulary

2

Types of Data

3

Samples

4

Conclusion

Vocabulary Types of Data Samples Conclusion

Important Concepts

Things to Remember from Section 9-1

1 Vocabular Terms: 1

sample vs. population

2

data and variable

3

discrete vs. continuous variables

2 Identifying simple random samples

Vocabulary Types of Data Samples Conclusion

Important Concepts

Things to Remember from Section 9-1

1 Vocabular Terms: 1

sample vs. population

2

data and variable

3

discrete vs. continuous variables

2 Identifying simple random samples

Vocabulary Types of Data Samples Conclusion

Important Concepts

Things to Remember from Section 9-1

1 Vocabular Terms: 1

sample vs. population

2

data and variable

3

discrete vs. continuous variables

2 Identifying simple random samples

Vocabulary Types of Data Samples Conclusion

Important Concepts

Things to Remember from Section 9-1

1 Vocabular Terms: 1

sample vs. population

2

data and variable

3

discrete vs. continuous variables

2 Identifying simple random samples

Vocabulary Types of Data Samples Conclusion

Important Concepts

Things to Remember from Section 9-1

1 Vocabular Terms: 1

sample vs. population

2

data and variable

3

discrete vs. continuous variables

2 Identifying simple random samples

Vocabulary Types of Data Samples Conclusion

Important Concepts

Things to Remember from Section 9-1

1 Vocabular Terms: 1

sample vs. population

2

data and variable

3

discrete vs. continuous variables

2 Identifying simple random samples

Vocabulary Types of Data Samples Conclusion

Next Time. . .

The next section deals with visually representations of data. In particular, we will look at two types of graphs: bar charts and pie charts. For next time Read section 9-2

Vocabulary Types of Data Samples Conclusion

Next Time. . .

The next section deals with visually representations of data. In particular, we will look at two types of graphs: bar charts and pie charts. For next time Read section 9-2