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
Slide 2
Investigation 6A Advanced Integrated Math I
Slide 3
Section 6.02 Advanced Integrated Math I
Slide 4
Without talking, write down your answer to the following
question: What generic term do you use for carbonated soft
drinks?
Slide 5
A frequency table lists categories and the number of
occurrences in each Example table:
Slide 6
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.
Slide 7
Find the mean, median, and mode for the following data set:
{20, 22, 22, 36, 42, 68}
Slide 8
Which measure(s) of center can be found for the soft drink
survey? What is the mean/median/mode for each state?
Slide 9
A class of 20 students takes a 5-question multiple choice test.
Each question is worth 20 points. Find the mean, median, and
mode.
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
Slide 12
Slide 13
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
Slide 14
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
Slide 15
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
Slide 16
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
Slide 17
Slide 18
Section 6.03 Advanced Integrated Math I
Slide 19
Place a dot above a number line for each data point. Example
for best actor winners (1986-2006):
Slide 20
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):
Slide 21
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):
Slide 22
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):
Slide 23
Create each of the following for the best actress winners ages.
Dot Plot Histogram Ordered stem and leaf plot
Finish making the dot plot, histogram, and ordered stem and
leaf plot that you started yesterday.
Slide 28
Slide 29
Slide 30
Section 6.04 Advanced Integrated Math I
Slide 31
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
Slide 32
Find the five-number summary for the life expectancy of males
in the countries listed in the table.
Slide 33
Find the five-number summary for the life expectancy of females
in the countries listed in the table.
Slide 34
Range = Maximum Minimum The range covers 100% of the data
Interquartile Range IQR = Q3 Q1 The IQR covers 50% of the data
Slide 35
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).
Slide 36
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.
Slide 37
Draw a box and whisker plot for the average life expectancy of
females from the previous you-try.
Slide 38
Put one box-and-whisker plot above another one on the same
number line.
Slide 39
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.
Slide 40
Read Section 6.04 (pages 495-499) Page 500 #6-11
Slide 41
Slide 42
Slide 43
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.
Slide 44
Slide 45
Slide 46
Section 6.05 Advanced Integrated Math I
Slide 47
Categorical variables takes on values that are words or
phrases, not numbers. The frequencies of categorical data are still
numbers.
Slide 48
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.
Slide 49
Displays the distribution for two categorical variables.
Example:
Slide 50
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.
Slide 51
1) What percent of non-athletes agreed with the statement? 2)
What percent of those who agreed with the statement were
non-athletes?
Slide 52
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.
Slide 53
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?
Slide 54
Consider a standard deck of cards. If a drawn card is a face
card, what is the probability that it is a jack?
Slide 55
Consider a standard deck of cards. If a drawn card is not a
jack, what is the probability that it is a face card?
Slide 56
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
Slide 57
See textbook for #8, 9, 11, 12
Slide 58
Slide 59
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.
Slide 60
New date and time Wednesday, February 25 Time TBD
Slide 61
Slide 62
Section 6.06 Advanced Integrated Math I
Slide 63
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.
Slide 64
Slide 65
On graph paper, create a scatter plot for the life expectancies
in the table. Describe any pattern you see in the scatter
plot.
Slide 66
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.
Slide 67
Why is there a positive association for male and female life
expectancies?
Slide 68
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
Slide 69
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.
Slide 70
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
Slide 71
Slide 72
Slide 73
Find the mean and the five-number summary for the following
data. 32, 25, 22, 19, 27, 27, 28, 30, 23, 32, 42, 26
Slide 74
Slide 75
[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]
Slide 76
Press [Y=] and clear all equations
Slide 77
Scatter plot Connected scatter plot Histogram Bin size set by
Xscl Modified box and whisker plot Box and whisker plot ?
Slide 78
On TI-84, create a scatter plot for the life expectancies in
the table.