Algebra I: Chapter 12 Notes

Probability and Statistics

Section 12-1, Day 1

Population –

Sample –

Simple Random Sample –

Bias –

Section 12-1, Day 1

Population – all members of a group of interest

Sample – some members of a group of interest

Simple Random Sample – each member in the population has the same chance of being chosen for the sample

Bias – an error because of misrepresentation of a population

Section 12-1, Day 1

Other Types of Samples:Systematic Sample Self-Selected Sample

Convenience Sample Stratified Sample

Section 12-1, Day 1

Other Types of Samples:Systematic Sample

Members are selected using a specific interval, such as every third person

Self-Selected Sample

Members volunteer to be included in the sample

Convenience Sample

Members are easy to reach for the sample

Stratified Sample

The population is first divided into groups, then members of each group are randomly chose for the sample

Section 12-1, Day 1

Example: Animals in a zoo are divided by species. Then two animals are selected at random from each group to have their blood tested. a) Identify the sample and population

b) Classify the sample as simple, systematic, convenience, or stratified. Explain.

Section 12-1, Day 1

Example 2: Identify each sample as biased or unbiaseda) Every 5th person coming into a grocery store

is asked to name their favorite radio station.

b) Every 5th person at the country music showcase is asked to name their favorite radio station

Section 12-1, Day 2Study Types

Type Definition Example

Survey Data are collected from responses from a sample regarding:

Asking students for their opinions on dance decorations

Observational Study

Members of a sample are observed… A gaming company watches a group of teens play a video game

Experiment The sample is divided into 2 groups:• An experimental group:

• A control group:

A teacher gives one Algebra class a pencil and paper test, and the other class a computer test covering the same information

Section 12-1, Day 2Study Types

Type Definition Example

Survey Data are collected from responses from a sample regarding:Characteristics, behaviors, or opinions

Asking students for their opinions on dance decorations

Observational Study

Members of a sample are observed…Without being affected by the study

A gaming company watches a group of teens play a video game

Experiment The sample is divided into 2 groups:• An experimental group: Undergoes

change• A control group: does not undergo

change

A teacher gives one Algebra class a pencil and paper test, and the other class a computer test covering the same information

Section 12-1, Day 2

Ex) Determine whether each situation is a survey, an observational survey, or an experiment. Explaina) A local charity is interested in finding out if residents would

use a curb-side service for donations. They distribute 30 questionnaires to people in the neighborhood.

b) A company shows 5 different commercials that advertise the same product. They record the students reaction to each.

Section 12-1, Day 2

Ex) Identify each survey question as biased or unbiased. If biased, explaina) Is your favorite ice cream plain vanilla or

delicious chocolate?

b) What types of reading material(s) do you enjoy?

Section 12-2, Day 1

Statistical Inference –

Statistic –

Parameter –

Section 12-2, Day 1

Statistical Inference – using statistics to draw conclusions

Statistic – measure that describes a characteristic of a sample

Parameter – a measure that describes a characteristic of a population

Section 12-2, Day 1

Ex) Identify the sample and population. Then describe the sample statistic and the population parameter.a) At a local university, a random sample of 40

scholarship applicants is selected. The mean GPA of the 40 applicants is calculated.

b) A stratified random sample of registered nurses is selected from all hospitals in a 3-county area, and the median salary is calculated.

Section 12-2, Day 1

Mean Absolute Deviation (MAD): The average of the absolute values of the differences between the mean and each value in the data set. The MAD predicts errors and and judges how well the mean represents the data.

Section 12-2, Day 1

Finding the MAD:1) Find the mean ( )2) Find the absolute value

of the difference of each data value and the mean

3) Find the sum of the values in step 2

4) Divide the sum by the number of values in the data set

Find the MAD of the set {2, 2, 3, 4, 14}

Section 12-2, Day 2

Standard Deviation – shows how the data deviate from the mean. Represented by the lowercase Greek symbol sigma σ

Variance – the square of standard deviation

Section 12-2, Day 2

Standard Deviation1) Find the mean2) Find the square of the

difference between each data value and the mean

3) Find the sum of the values in step 2

4) Divide the sum by the number of values

5) Take the square root of the number in step 4

Find the standard deviation and variance of the data set:{9, 10, 11, 6, 9, 11, 9, 8, 11, 8, 7, 9, 11, 11, 5}

Section 12-2, Day 2

Cont…Find the standard deviation and variance of the data set: {9, 10, 11, 6, 9, 11, 9, 8, 11, 8, 7, 9, 11, 11, 5}

Section 12-3, Day 1

Distribution of Data

Section 12-3, Day 1

Ex1) Use the data to construct a histogram for the data, and describe the shape of the distribution{25, 22, 31, 25, 26, 35, 18, 39, 22, 32, 34, 26, 42, 23, 40, 36, 18, 30, 26, 30, 37, 23, 19, 33, 24, 29, 39, 21, 43, 25, 34, 24, 26, 30, 21, 22}

Use this page for your histogram

Section 12-3, Day 1

Ex2) Use the data to construct a histogram for the data, and describe the shape of the distribution{9, 17, 15, 10, 16, 2, 17, 19, 10, 18, 14, 8, 20, 20, 3, 21, 12, 11, 5, 26, 15, 28, 12, 5, 27, 26, 15, 53, 12, 7, 22, 11, 8, 16, 22, 15}

Use this page for your histogram

Section 12-4, Day 1: Transformation of Data

Ex1) Find the mean, median, mode, range, and standard deviation of the data set {13, 5, 8, 12, 7, 4, 5, 8, 14, 11, 13, 8}Mean:

Median:

Mode:

Range:

SD:

Section 12-4, Day 1: Transformation of Data

Now add 7 to each value and find the mean, median, mode, range and standard deviation of the data set from the previous slide {13, 5, 8, 12, 7, 4, 5, 8, 14, 11, 13, 8}Mean:

Median:

Mode:

Range:

SD:

Section 12-4, Day 1

If a number k is added or subtracted to every value in the data set, what happens to the:Mean:Median:Mode:Range:Standard Deviation:

Section 12-4, Day 1: Transformation of Data

Ex1) Find the mean, median, mode, range, and standard deviation of the data set {21, 12, 15, 18, 16, 10, 12, 19, 17, 18, 12, 22}Mean:

Median:

Mode:

Range:

SD:

Section 12-4, Day 1: Transformation of Data

Now multiply each value by 3 then find the mean, median, mode, range, and standard deviation of the data set {21, 12, 15, 18, 16, 10, 12, 19, 17, 18, 12, 22}Mean:

Median:

Mode:

Range:

SD:

Section 12-4, Day 1

If a number k (when k > 0) is multiplied to every value in the data set, what happens to the:Mean:Median:Mode:Range:Standard Deviation:

Section 12-4, Day 1: Comparing Data

Below are quiz scores for two students, Kody and Tori. On the next 2 slides you will construct a histogram for each data set and describe the shape of each distribution.

Kody: 85, 95, 70, 87, 78, 82, 84, 84, 85, 99, 88, 74, 75, 89, 79, 80, 92, 91, 96, 81

Tori: 89, 76, 87, 86, 92, 77, 78, 83, 83, 82, 81, 82, 84, 85, 85, 86, 89, 93, 77, 85

Use this page for your histogram (Kody’s Quiz Scores)

Use this page for your histogram:(Tori’s Quiz Scores)

Section 12-4, Day 1

Using the quiz data, compare the mean and standard deviation for Kody and Tori.Kody

ToriMean:Mean:

Standard Deviation: Standard Deviation: