Chapter 12 Sections 4/5
Algebra 2 Notes ~ February 17, 2009


Warm-Ups
Copy the following table:
Right Handed
Right Shoe 1st
Left Shoe 1st
1st One Grabbed
Don’t Know
Left Handed

Ask 10 different people in the class what their dominate hand is and which shoe they put on first. Fill out the table.

Find each probability:

Chapter 12 Section 4
Standard Deviation

Measures of Variation

Range of a set of data: the difference between the greatest and least values in the data set

Interquartile Range: the difference between the third and first quartiles.

Measures of Variation

Thirteen men qualified for the 2002 U.S. Men’s Alpine Ski
Team. Find the range and the interquartile range of their ages at the time of qualification:
27, 28, 29, 23, 25, 26, 26, 28, 22, 23, 23, 21, 25
STEP 1: Find quartiles 1, 2, 3, and 4 of the data

Standard Deviation
 the mean of the data set
 n = the number of values in the data set
 the difference between each value and the mean

The symbol means “sum”

Finding the Standard Deviation

Find the mean and the standard deviation for the values 48.0,
53.2, 52.3, 46.6, 49.9.

First find the mean ( ).

Organize the info into a table:

Finding the Standard Deviation

Find the mean and the standard deviation for the values 50, 60, 70, 80, 80, 90, 100, 110.

Using Standard Deviation

Look at page 670 Example #3; use the table of values of
Daily Energy Demand During August. The mean of these values is 43.2 and the standard deviation is about 6.0.
Within how many standard deviations of the mean to all the values fall?

Using Standard Deviation

In May, the mean daily energy demand is 35.8 MWh, with standard deviation of 3.5 MWh. The power company prepares for any demand within three standard deviation of the mean. Are they prepared for a demand of 48
MWh? Explain.

Finding the z-score

Z-score: the number of standard deviations that a value from the data set is from the mean

A set of values has a mean of 85 and a standard deviation of 6. Find the z-score of the value 76.

Find the value that has a z-score of 2.5

Chapter 12 Section 5
Working With Samples

Sample Proportions

Sample: gathers information from only part of a population

Sample Proportion =

 x is the number of times an event occurs n is the sample size

Example: In a sample of 350 teenagers, 294 have never made a snow sculpture. Find the sample proportion for those who have never made a snow sculpture.

Sample Proportions

Two major factors that influence the reliability of samples:
1.
Sampling Bias
2.
Sample Sizes

Bias in Sampling

Bias: To show favoritism in a person or thing; to influence unfairly; prejudice




A news program reports on a proposed school dress code.
The purpose of the program is to find what percent of the population in its viewing area favors the dress code. Discuss the bias in the three types of sampling methods.
Viewers are invited to call in and express their preferences
A reporter interviews people on the street near the local high school
During the program, 300 people are selected at random from the viewing area. Then each person is contacted.

Comparing Sampling Sizes


Using the Margin of Error

The larger the sample size, the smaller the margin of error


Example: A recent poll reported that 56% of voters favored President Obama’s Stimulus Plan, with a margin of error of . Estimate the number of participants in the poll.
Use the margin of error to determine the likely range for the true population proportion

Using the Margin of Error

Example 2: A survey of 2580 students found that 9% are left-handed.

Find the margin of error for the sample

Use the margin of error to find the interval that is likely to contain the population proportion

Homework #25

Pg 672 #1, 2, 4, 5, 8, 15, 21

Pg 680 #1, 2, 4, 5, 8-10, 12, 13, 16, 18, 20,
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