Statistics is the branch of mathematics that deals with collecting, organizing, analyzing, and...

Statistics is the branch of mathematics that deals with collecting, organizing, analyzing, and reporting quantitative information.

Statistics is the branch of mathematics that deals with collecting, organizing, analyzing, and reporting quantitative information.

StatisticsStatistics

Recorded observations that can be measured or countedRecorded observations that can be measured or counted

DataData

A population is an entire set of objects sharing similar characteristics, such as human beings, automobiles, or measurements, from which data can be collected and analyzed.

A population is an entire set of objects sharing similar characteristics, such as human beings, automobiles, or measurements, from which data can be collected and analyzed.

PopulationPopulation

A sample is a portion of a population from which data is collected to estimate the characteristics of the entire population.

A sample is a portion of a population from which data is collected to estimate the characteristics of the entire population.

SampleSample

A statistic is a measure calculated from a sample of data.

A statistic is a measure calculated from a sample of data.

StatisticStatistic

A parameter is a measure calculated from data for an entire population.

A parameter is a measure calculated from data for an entire population.

ParameterParameter

populationAll snacks are being

considered.

populationAll snacks are being

considered.

Example 1Example 1Identify as a sample or a population: the snacks dispensed from a vending machine during its existence.

Identify as a sample or a population: the snacks dispensed from a vending machine during its existence.

sampleA small number of students

is being considered.

sampleA small number of students

is being considered.

Identify as a sample or a population: 100 freshman from among those enrolled at a local college for the fall of 2010.

Identify as a sample or a population: 100 freshman from among those enrolled at a local college for the fall of 2010.

Example 1Example 1

populationAll of the automobiles

produced by the company are being considered.

populationAll of the automobiles

produced by the company are being considered.

Identify as a sample or a population: the automobiles built by General Motors in the 1990s.

Identify as a sample or a population: the automobiles built by General Motors in the 1990s.

Example 1Example 1

populationpopulation

Identify as a sample or a population: a school official gathers data about all students at Union University when studying the majors offered at the university.

Identify as a sample or a population: a school official gathers data about all students at Union University when studying the majors offered at the university.

ExampleExample

samplesample

Identify as a sample or a population: a magazine wishes to determine the political viewpoint of college students, so it sends a questionnaire to all students at Union University.

Identify as a sample or a population: a magazine wishes to determine the political viewpoint of college students, so it sends a questionnaire to all students at Union University.

ExampleExample

Four Types of Population Sampling

Four Types of Population Sampling

1. Random—A random number generator is used to determine page number, column, and row of each person in the sample.

2. Systematic—Every thirtieth person listed in the phone book is included in the sample.

3. Convenience—A questionnaire with a return envelope is mailed out with the phone bill.

4. Cluster—Everyone whose address indicates that he lives in a particular section of town is included in the sample.

convenienceconvenience

Identify the sample as random, systematic, convenience, or cluster: math teachers who attend a workshop at the regional conference.

Identify the sample as random, systematic, convenience, or cluster: math teachers who attend a workshop at the regional conference.

Example 2Example 2

systematicsystematic

Identify the sample as random, systematic, convenience, or cluster: every fifth person on the class roster.

Identify the sample as random, systematic, convenience, or cluster: every fifth person on the class roster.

Example 2Example 2

randomrandom

Identify the sample as random, systematic, convenience, or cluster: 500 voters, based on phone numbers chosen by computer-generated selection of page number and column in the phone book.

Identify the sample as random, systematic, convenience, or cluster: 500 voters, based on phone numbers chosen by computer-generated selection of page number and column in the phone book.

Example 2Example 2

systematicsystematic

Identify the sample as random, systematic, convenience, or cluster: A worker selects the first phone number from every page of the phone book for a phone survey.

Identify the sample as random, systematic, convenience, or cluster: A worker selects the first phone number from every page of the phone book for a phone survey.

ExampleExample

clustercluster

Identify the sample as random, systematic, convenience, or cluster: To evaluate rates for the countywide school system, the school board randomly selects two high schools and evaluates the data at those two schools.

Identify the sample as random, systematic, convenience, or cluster: To evaluate rates for the countywide school system, the school board randomly selects two high schools and evaluates the data at those two schools.

ExampleExample

The range is the difference between the largest and smallest numbers in a set of data.

The range is the difference between the largest and smallest numbers in a set of data.

RangeRange

The mean is the arithmetic average of a set of numbers (sum of data divided by the number of data).

The mean is the arithmetic average of a set of numbers (sum of data divided by the number of data).

MeanMean

The median is the middle number in a set of data arranged in numerical order. If there is an even number of data, the median is the average of the two middle numbers.

The median is the middle number in a set of data arranged in numerical order. If there is an even number of data, the median is the average of the two middle numbers.

MedianMedian

The mode is the number or numbers that occur most frequently in a set of data. If no number occurs more than once, there is no mode. Data sets in which two values occur most frequently are called bimodal, while other data sets may have no mode.

The mode is the number or numbers that occur most frequently in a set of data. If no number occurs more than once, there is no mode. Data sets in which two values occur most frequently are called bimodal, while other data sets may have no mode.

ModeMode

Mean Average Mean Average

Median MiddleMedian Middle

Mode Most Mode Most

= 7= 7

Find the range, mean, median, and mode of the following set of data: {6, 9, 7, 3, 6, 7, 10, 5}.

Find the range, mean, median, and mode of the following set of data: {6, 9, 7, 3, 6, 7, 10, 5}.10, 9, 7, 7, 6, 6, 5, 310, 9, 7, 7, 6, 6, 5, 3range: 10 – 3range: 10 – 3mean: sum of data = 53mean: sum of data = 53

average = 53 ÷ 8average = 53 ÷ 8 ≈ 6.6≈ 6.6

Example 3Example 3

Find the range, mean, median, and mode of the following set of data: {6, 9, 7, 3, 6, 7, 10, 5}.

Find the range, mean, median, and mode of the following set of data: {6, 9, 7, 3, 6, 7, 10, 5}.median: 10, 9, 7, 7, 6, 6, 5, 3median: 10, 9, 7, 7, 6, 6, 5, 377 66

7 + 62

7 + 62

132

132

== = 6.5= 6.5

6 and 76 and 7mode:mode:

= 22= 22

Find the range, mean, median, and mode of the following set of data: {58, 38, 60, 44, 45, 42, 49, 50, 41}.

Find the range, mean, median, and mode of the following set of data: {58, 38, 60, 44, 45, 42, 49, 50, 41}.

38, 41, 42, 44, 45, 49, 50, 58, 60

38, 41, 42, 44, 45, 49, 50, 58, 60

range: 60 – 38range: 60 – 38

Example 4Example 4

Find the range, mean, median, and mode of the following set of data: {58, 38, 60, 44, 45, 42, 49, 50, 41}.

Find the range, mean, median, and mode of the following set of data: {58, 38, 60, 44, 45, 42, 49, 50, 41}.

median: 38, 41, 42, 44, 45, 49, 50, 58, 60median: 38, 41, 42, 44, 45, 49, 50, 58, 60

4545

nonenonemode:mode:

mean: sum of data = 427mean: sum of data = 427average = 427 ÷ 9average = 427 ÷ 9 ≈ 47.4≈ 47.4

The following are daily low temperatures from the preceding week. Find the range, mean, median, and mode of the temperatures.

The following are daily low temperatures from the preceding week. Find the range, mean, median, and mode of the temperatures.

Example 5Example 5

DayMondayTuesday

Wednesday Thursday

FridaySaturday Sunday

DayMondayTuesday

Wednesday Thursday

FridaySaturday Sunday

Temperature (°F)25°21°20° 29°25°22° 19°

Temperature (°F)25°21°20° 29°25°22° 19°

median: 29, 25, 25, 22, 21, 20, 19median: 29, 25, 25, 22, 21, 20, 19

2222

25°25°mode:mode:

mean: sum of data = 161mean: sum of data = 161average = 161 ÷ 7average = 161 ÷ 7 = 23°= 23°

= 10°= 10°range: 29 – 19range: 29 – 1929, 25, 25, 22, 21, 20, 1929, 25, 25, 22, 21, 20, 19

Use this data to solve the following problems:

A = {13, 25, 22, 18, 17, 17, 14, 16, 22}

B = {19, 22, 35, 39, 35, 37, 40, 100}

Use this data to solve the following problems:

A = {13, 25, 22, 18, 17, 17, 14, 16, 22}

B = {19, 22, 35, 39, 35, 37, 40, 100}

ExampleExample

Arrange the data for each set in ascending order.Arrange the data for each set in ascending order.

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

ExampleExample

Find the range of each set.Find the range of each set.

A: 12; B: 81A: 12; B: 81

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

ExampleExample

Find the median of each set.Find the median of each set.

A: 17; B: 36A: 17; B: 36

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

ExampleExample

Find the mode of each set.Find the mode of each set.

A: 17 and 22; B: 35A: 17 and 22; B: 35

ExampleExample

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

Find the mean of each set.Find the mean of each set.

A: 18.22; B: 40.875A: 18.22; B: 40.875

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

B = {19, 22, 35, 35, 37, 39, 40, 100}

ExampleExample

Would changing a single value in A always change the mean? Is this true for any set of data?

Would changing a single value in A always change the mean? Is this true for any set of data?

yes; yesyes; yes

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

ExampleExample

Would changing a single value in A always change the median?

Would changing a single value in A always change the median?

nono

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

A = {13, 14, 16, 17, 17, 18, 22, 22, 25}

ExampleExample

If C = {12, 13, 14}, does C have three modes or no modes?

If C = {12, 13, 14}, does C have three modes or no modes?

no modesno modes

ExampleExample