Trigonometry Chapter 11 Section 1

GUIDED PRACTICE for Example 1 TRANSPORTATION 1. The data set below gives the waiting times (in minutes) of 10 students waiting for a bus. Find the mean, median, and mode of the data set. 4, 8, 12, 15, 3, 2, 6, 9, 8, 7

GUIDED PRACTICE for Examples 2 and 3 Find the range and standard deviation of the data set. 4, 8, 12, 15, 3, 2, 6, 9, 8, 7

Mean 14 13 Median 14.5 Mode 15 Range 6 S.D. 1.7 3.5 Outlier An outlier is value that is much greater or much less than most of the other values in a data set. So, here is the comparison…. Mean 14 13 Median 14.5 Mode 15 Range 6 S.D. 1.7 3.5

EXAMPLE 4 Examine the effect of an outlier Air Hockey You are competing in an air hockey tournament. The winning scores for the first 10 games are given below. 14, 15, 15, 17, 11, 15, 13, 12, 15, 13 Find the mean, median, mode, range,and standard deviation of the data set. b. The winning score in the next game is an outlier, 3. Find the new mean, median, mode, range, and standard deviation. c. Which measure of central tendency does the outlier affect the most? the least? What effect does the outlier have on the range and standard deviation?

EXAMPLE 4 Examine the effect of an outlier Here is the data in order: 11, 12, 13, 13, 14, 15, 15, 15, 15, 17 Find the mean, median, mode, range,and standard deviation of the data set.

EXAMPLE 4 Examine the effect of an outlier b. The winning score in the next game is an outlier, 3. Find the new mean, median, mode, range, and standard deviation.

GUIDED PRACTICE for Example 4 3. What If? In part (b) of Example 4, suppose the winning score in the next game is 25 instead of 3. Find the new mean, median, mode, range, and standard deviation of the data set . Here is the data in order: 11, 12, 13, 13, 14, 15, 15, 15, 15, 17

Trigonometry Chapter 11 Section 3

Normal Curve A Normal Distribution with mean, x, and standard deviation, σ, has the following properties: The total area under the related normal curve is 1. About 68% of the area lies within 1 standard deviation of the mean. About 95% of the area lies within 2 standard deviations of the mean. About 99.7% of the area lies within 3 standard deviations of the mean.

Notice they have divided their standard deviations by .5!!!! Normal Curve from the Regents Reference Sheet Notice they have divided their standard deviations by .5!!!!

GUIDED PRACTICE for Examples 1 and 2 The blood cholesterol readings for a group of women are normally distributed with a mean of 172 mg/dl and a standard deviation of 14 mg/dl. - what percent of the women have readings between 172 and 200? 47.7% ANSWER

Normal Curve from the Regents Reference Sheet

Trigonometry Chapter 11 Section 4

Samples/Populations A Population is a group of people or objects that you want information about. A Sample is a subset of the population that you actually collect the information from. Samples can be: Self-selected Systematic Convenience Random

EXAMPLE 1 Classify samples Baseball A sportswriter wants to survey college baseball coaches about whether they think wooden bats should be mandatory throughout college baseball. Identify the type of sample described. The sportswriter contacts only the coaches that he has cell phone numbers for in order to get quick responses. Self-selected Systematic Convenience Random The sportswriter mails out surveys to all the coaches and uses only the surveys that are returned. Self-selected Systematic Convenience Random

EXAMPLE 2 Identify a biased sample Concert Attendance The manager of a concert hall wants to know how often people in the community attend concerts. The manager asks 50 people standing in line for a rock concert how many concerts per year they attend. Tell whether the sample is biased or unbiased. Explain your reasoning.

EXAMPLE 3 Choose an unbiased sample Senior Class Prom You are a member of the prom committee. You want to poll members of the senior class to find out where they want to hold the prom. There are 324 students in the senior class. Describe a method for selecting a random sample of 40 seniors to poll.

GUIDED PRACTICE for Examples 1, 2, and 3 SCHOOL WEBSITE: A computer science teacher wants to know if students would like the morning announcements posted on the school’s website. He surveys students in one of his computer science classes. Identify the type of sample described, and tell whether the sample is biased.

Is this sample biased or unbiased? Is it: A survey is conducted by calling randomly selected phone numbers at 1:00 PM during the week. Is this sample biased or unbiased? Is it: Self-selected Systematic Convenience Random Are the following questions biased or unbiased? What is your height in inches? Should motorcycle helmets be mandatory to save lives?

Controlled/Observation/Survey

Controlled/Observation/Survey A researcher conducts an experiment to see if a new medication is effective in preventing strokes. An experimental group of accountants suffers more strokes than a control group of professional baseball players. Identify any flaws in this experiment and describe how they can be corrected.

Trigonometry Chapter 11 Section 4

GUIDED PRACTICE for Examples 1 and 2 Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane. 1.

GUIDED PRACTICE for Examples 1 and 2 2.

EXAMPLE 3 Use a quadratic model Fuel Efficiency A study compared the speed x (in miles per hour) and the average fuel efficiency y (in miles per gallon) of cars. The results are shown in the table. Use a graphing calculator to find a model for the data.

GUIDED PRACTICE for Example 3 Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane. 4.

GUIDED PRACTICE for Example 3 5.