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Sophia claims that the typical winner of the Best Actor award is much older than the typical winner of the Best Actress award. Make some arguments that support or oppose Sophias claim. YearActorAgeActressAge 1986Paul Newman61Marlee Matlin21 1987Michael Douglas43Cher41 1988Dustin Hoffman51Jodie Foster26 1989Daniel Day-Lewis32Jessica Tandy80 1990Jeremy Irons42Kathy Bates42 1991Anthony Hopkins54Jodie Foster29 1992Al Pacino52Emma Thompson33 1993Tom Hanks37Holly Hunter35 1994Tom Hanks38Jessica Lange45 1995Nicolas Cage31Susan Sarandon49 1996Geoffrey Rush45Frances McDormand39 1997Jack Nicholson60Helen Hunt34

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Investigation 6A Advanced Integrated Math I

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Section 6.02 Advanced Integrated Math I

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Without talking, write down your answer to the following question: What generic term do you use for carbonated soft drinks?

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A frequency table lists categories and the number of occurrences in each Example table:

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Arithmetic Mean: Add the values and divide by the number of values. Median: The middle number when data is arranged in order. If there are two middle values, find the mean of those two numbers. Mode: The data value that occurs most often.

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Find the mean, median, and mode for the following data set: {20, 22, 22, 36, 42, 68}

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Which measure(s) of center can be found for the soft drink survey? What is the mean/median/mode for each state?

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A class of 20 students takes a 5-question multiple choice test. Each question is worth 20 points. Find the mean, median, and mode.

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Page 479 #3, 4, 6, 7 Read Section 6.02 (pages 481-484) Page 485 #5, 6, 8, 9, 10

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3) Describe how to find each measure for seven test scores. What does each measure tell you? a.Mean b.Median c.Mode 4) Milo sits next to a tollbooth and counts the number of people in each of 50 cars. He records his findings in the table. Then Milo calculates the mean number of people in each car. a.Whats wrong here? On his first try, Milo finds the mean of the five numbers, 31, 12, 3, 2, and 2, to be 10. Explain why this cannot be the mean number of people in each car. b.Find the correct mean number of people in each car. See textbook for #6, 7 Number of People in Car Number of Cars 131 212 33 42 52

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Find a convenient and easy to understand way to display the following data: 41, 37, 59, 65, 44, 49, 52, 44, 61, 72, 72, 43, 25, 49, 36, 29, 24, 63, 20, 88, 27, 50, 61, 71, 36, 80, 38 Period 2

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Find a convenient and easy to understand way to display the following data: 36, 70, 79, 53, 43, 55, 59, 25, 36, 58, 57, 39, 21, 50, 30, 51, 46, 34, 33, 95, 77, 53, 64 Period 3

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Find a convenient and easy to understand way to display the following data: 38, 69, 61, 55, 4, 64, 29, 45, 40, 52, 53, 26, 39, 52, 45, 45, 19, 64, 69, 58, 59, 55, 29, 67, 49, 28, 56 Period 5

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Warm-Up: Create a better way to display the data. It should be easier to see the center, spread, and shape of the ages. Table on page 478

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Section 6.03 Advanced Integrated Math I

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Place a dot above a number line for each data point. Example for best actor winners (1986-2006):

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A histogram is like a bar graph where frequencies are grouped into intervals called bins. There are no gaps between bins or bars (except bars of zero height). Bins can be of any width Examples for best actor winners (1986-2006):

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The first digit(s) are listed in order in the stem. To the side, the remaining digits are listed. Example for best actor winners (1986-2006):

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A stem and leaf plot where the leaves are also in numerical order Very helpful for finding the median Example for best actor winners (1986-2006):

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Create each of the following for the best actress winners ages. Dot Plot Histogram Ordered stem and leaf plot

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Read section 6.03 (pages 488-490) Page 491 #4-9, 11

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Finish making the dot plot, histogram, and ordered stem and leaf plot that you started yesterday.

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Section 6.04 Advanced Integrated Math I

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Minimum: The lowest value First Quartile (Q1): The data value the lowest 25% of data values. The middle value of the first half of sorted data Median: The data value the lowest 50% of data values. The middle value of the sorted data set Third Quartile (Q3): The data value the lowest 75% of data values. The middle value of the second half of sorted data Maximum: The greatest value

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Find the five-number summary for the life expectancy of males in the countries listed in the table.

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Find the five-number summary for the life expectancy of females in the countries listed in the table.

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Range = Maximum Minimum The range covers 100% of the data Interquartile Range IQR = Q3 Q1 The IQR covers 50% of the data

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How far away from other points must a point lie to be considered an outlier? 1.5 times the IQR away from the nearest quartile (Q1 or Q3).

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1) Find the five-number summary. 2) At each of the five numbers, draw a short vertical line segment above a number line. 3) Draw a box from Q1 to Q3, with median inside. 4) Draw horizontal line segments (whiskers) to connect the box to the minimum and maximum.

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Draw a box and whisker plot for the average life expectancy of females from the previous you-try.

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Put one box-and-whisker plot above another one on the same number line.

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The paired box-and-whisker plots show the test scores from two different classes on the same test. Based on the data, in which class would you prefer to be. Explain.

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Read Section 6.04 (pages 495-499) Page 500 #6-11

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A teacher conducted a survey of her students, both athletes and non-athletes. She recorded their response (agree or disagree) to the statement, Classes should start and end one hour later. Find a way to organize the responses numerically.

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Section 6.05 Advanced Integrated Math I

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Categorical variables takes on values that are words or phrases, not numbers. The frequencies of categorical data are still numbers.

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1) Write a ratio of the number of athletes who agree with the statement to the total number of athletes. 2) Write a ratio of the number of athletes who agree with the statement to the total number of students who agree with the statement.

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Displays the distribution for two categorical variables. Example:

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The survey from the warm-up was given to more students at the school, producing the following data: 1) Write a ratio of the number of athletes who agree to the total number of athletes. 2) Write a ratio of the number of students surveyed who agree to the total number of students surveyed.

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1) What percent of non-athletes agreed with the statement? 2) What percent of those who agreed with the statement were non-athletes?

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There is an association, also called correlation, between two variables if changing the distribution of one variable significantly changes the distribution of the other variable. In the survey, non-athletes were more likely than athletes to agree, so there was an association. If you ask more non-athletes, the overall percentage of agrees would also increase. Variables that are not associated are called independent.

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Tess makes the following comment about the survey: 31 athletes agreed with the idea, but only 23 non-athletes agreed. It looks like athletes are more likely to agree, which surprises me. Give an argument supporting or rejecting Tesss claim. Are athletes actually more likely to agree than non-athletes?

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Consider a standard deck of cards. If a drawn card is a face card, what is the probability that it is a jack?

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Consider a standard deck of cards. If a drawn card is not a jack, what is the probability that it is a face card?

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Read section 6.05 (pages 503-506) Page 508 #8, 9, 11, 12, 13, 14 #8, 9, 11, 12 refer to the chart on page 508

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See textbook for #8, 9, 11, 12

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Punxsutawney Phil, seer of seers, prognosticator of prognosticators, has been predicting the end of winter for over 100 years. In that time, he has predicted 6 more weeks of winter 98 times, an early spring 15 times, and there is no record of 10 of his predictions. 1) Is the data quantitative or categorical? 2) Create an appropriate display of the data.

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New date and time Wednesday, February 25 Time TBD

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Section 6.06 Advanced Integrated Math I

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Bivariate data is data for two related variables. Examples: Male life expectancy and female life expectancy Height and weight Homework percentage and test percentage The two data sets can be plotted together in a scatter plot.

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On graph paper, create a scatter plot for the life expectancies in the table. Describe any pattern you see in the scatter plot.

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When you can see a pattern in a scatter plot, there is an association between the variables. Two variables are positively associated if large values of one are paired with large values of the other. Two variables are negatively associated if large values of one are paired with small values of the other.

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Why is there a positive association for male and female life expectancies?

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The correlation coefficient is a measure of how strongly associated two variables are. The linear correlation coefficient, r, is a measure of how close all of the data is to a straight line. -1 r1

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Correlation does not imply causation. Example: There is a strong correlation between the amount of ice cream sold at a beach on a given day and the number of lifeguard rescues at the beach on that day.

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Read Section 6.06 (pages 511-514) Page 516 #6, 7, 8, 10, 12 Scatter plot for #6 must be on graph paper. Page 520 #1-6

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Find the mean and the five-number summary for the following data. 32, 25, 22, 19, 27, 27, 28, 30, 23, 32, 42, 26

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[ON], [STAT], [1:Edit] Move cursor to L1 and press [CLEAR], [ENTER] Type the numbers into the L1 column, pressing [Enter] after each one 32, 25, 22, 19, 27, 27, 28, 30, 23, 32, 42, 26 Press [2nd], [MODE] to return to the home screen Press [STAT], [ CALC], [1:1-Var Stats], [2nd], [1], [ENTER]

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Press [Y=] and clear all equations

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Scatter plot Connected scatter plot Histogram Bin size set by Xscl Modified box and whisker plot Box and whisker plot ?

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On TI-84, create a scatter plot for the life expectancies in the table.

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Investigation 6A Reflections Page 520 #1-6

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See textbook for #6