SHOW
104
PROGRAM
SYNOPSIS
Whom Do You Ask?
Understanding Surveys
Segment 1 (7:02)
CALLOUS CANDY–
PARTS I, II, AND III
J. R. Callous, head of the
Callous Candy Company,
wonders why his gumdrops
are selling so poorly in his
hometown of Grasshopper
Gulch, so he decides to do
a survey of the townsfolk to
find out. After the results
of one survey are rejected
because the sample used
was too small and unrepresentative of the whole
population, he and his
family conduct another poll.
The results of that survey,
which are displayed on a
circle graph, suggest a way
to boost the sales of J.R.’s
product.
Segment 2 (3:03)
FAX HEADFULL:
HANDEDNESS
Fast-talking computergenerated talking head
Fax Headfull asserts that
left-handers comprise about
, or 10 percent, of the
world’s population—
about 530 million people.
He suggests that viewers
find out what percentage
of their own group are
left-handed.
INTRODUCTION
C
onducting surveys (or polls) is one important use of probability and
statistics. This tape shoes how a survey might be done and illustrates how
people can use the results of a survey to decide on a course of action.
RE
BEFO
VIEWING
Both segments on the tape use the language of percents, although
only a minimal acquaintance with percents is needed to understand
this material. You might want to review briefly the idea of 10
percent as and 50 percent as with students, if necessary.
R
AFTE
VIEWING
Discuss with students how Fax Headfull probably arrived at his
figure: Do they think that someone actually asked all the people in
the world about their handedness?
Take the poll of your students that is suggested by Fax
Headfull to see how well the number of left-handers in your
class agrees with the 10 percent figure that Fax claims is true
of the general population.
27
If your class
happens to have a
number of students that is
a multiple of 10, (20 or 30
students, for instance), 10%
of the class will be a
whole number.
MathTalk
If your students are familiar with decimals, you can do the
calculations exactly. For example, suppose there are 28
students. Then 10 percent of 28 is 2.8. If you have three
southpaws, that’s a little more than 10 percent. (Of course,
you could use a calculator to divide 3 by 28; that’s about 10.7
percent.) You can round the number of students in your
class up (and then down) to the nearest multiple of 10 and
find of each. The actual number of left-handers in your
class can then be compared to see if your group of lefties is
close to the 10 percent that Fax Headfull claims.
In any case, it’s worth stressing Fax’s point that the larger the
sample, the closer the fraction of left-handers is likely to be to
the fraction of left-handers in the whole population.
activity
MAKING CIRCLE GRAPHS
Y
our students can make their own circle graphs using the special
protractors on the reproducible page. Ordinary protractors are marked in
degrees, so if you want to use one to make a circle graph, you have to
convert percentages into degrees. This is confusing for students who are
just learning about percents. To get around this difficulty, the protractor on
page 32 is divided into 100 parts of equal size, each corresponding to one
percent. You may find it useful to construct for yourself a larger version of
the special protractor for use at the board. It doesn’t need to have every
percent marked on it. Just the marks for 10 percent, 20 percent, and so on,
will be enough.
1.
Before you duplicate the reproducible page, decide whether you
want to deal with percents or fractions, writing either “%”or “/100”
after each number on the protractor. (We suggest you use
percents even if they are relatively new to your students, but
if you think that will be too difficult, interpret the marks on
the protractor as hundredths.)
MATERIALS
For each student:
■ copies of reproducible page 32
■ scissors
Of course,
these numbers are made
up; you should figure out
the real percents for
your own class.
2. Distribute copies of the reproducible page and ask
students to cut out the special protractor. The
protractor is the same size as the empty circles on the
page, so it can be used to create circle graphs easily.
3.
28
Guide your students through one exercise in
constructing a circle graph so that they will see
how to use the protractor. You can use any
data you wish—for instance, the percentages
of the school day spent on various activities.
SCHOOL DAY
DATA:
READING
30%
MATHEMAT
ICS 20%
SCIENCE
15%
SOCIAL STUD
IES 15%
LUNCH
12%
RECESS
8%
P R O BAB I L I TY AN D STATI STI CS
Here are two ways
to use the protractor,
both of which work well.
0
100
a. Rotate the protractor between each
80
10
20
70
90
30
section of the graph, starting from 0
each time. To show the school data on
the previous page, you’d make marks
on your blank circle at 0 and 30 for
reading, and then turn the protractor
so that mathematics would go from
0 to 20, and so on.
Or:
b. Leave the protractor stationary on
your blank circle. Make marks for
reading at 0 and 30, and then a mark
for mathematics at 50, and so on, as
shown.
40
60
50
Then:
■ Draw line segments from the center
outward to the circle, going through
each of the dots that you drew.
D
TIME I SPEN
HOW MUCH S ACTIVITIES
ON VARIOUSCHOOL DAY
DURING A
■ Finally, label the sections of your
circle graph and give the graph
a title.
4. Once your students have had some
SOCIAL
STUDIES
15%
SCIENCE
15%
READING
30%
RE
CE
8% SS
LUNCH
12%
MATH
20%
practice with the special protractor,
they’ll be able to use it in all sorts of
situations. Your students might
want to use the extra blank circles
on the reproducible page to show
school demographic data or data
from preference surveys (similar to
the Callous graph).
Data from social studies are often
well represented by circle graphs.
For example, the percentages
of the area of a state that are forest,
farmland, urban development, water,
and so on are appropriate data for
circle graphs. Data for two different
states can be compared by using
two circle graphs side by side.
29
MathTalk
keep
thinking
PRESIDENTIAL HANDEDNESS
Fax Headfull discusses the handedness of presidents by looking at a
rather small sample.What would happen if a larger group of U.S.
presidents were considered? Who were all of the presidents, and what
were their handednesses? The figure for the larger group of all
presidents is likely to be much closer to the real level of left-handedness
in the whole population, unless, of course, there is some genuine
connection between left-handedness and political success. (The lefthanded presidents have been Garfield, Hoover,Truman, Ford,
Reagan, Bush, and Clinton. Seven out of 42 is about 17
percent. That’s quite a bit more than the 10 percent that
Fax claims for the general population. How might this be
explained? Is it just chance?)
The fraction of left-handed presidents from the 18th and
19th centuries is much smaller than the fraction of lefthanded presidents from the 20th century. Why? It may
be a result of changing attitudes toward left-handedness
over the years. Was more done a century ago than now
to discourage left-handers and to force them to write with
their right hands?
DRAWING CONCLUSIONS FROM STATISTICS
Alert students to uses of
graphic displays of surveys in the
media so they can record and reflect
on them in their journals.
30
About 10 years ago, a researcher at the University of British
Columbia named Stanely Coren did a survey of handedness. He
found that 15 percent of 10-year-olds, five percent of 50-year-olds,
and one percent of people 80 years old or older were left-handed.
(Stanley Coren, The Left-Hander Syndrome, MacMillan, Inc.,
1992.) What might account for the decline in the percentage of
left-handers with increasing age? (One possibility is that lefthanders die at a younger age. Another is that, in the past, lefthandedness was discouraged. Or maybe a lot of people who are
left-handed at an early age shift to being right-handed when they
get older. And there’s always the possibility that something was
wrong with his survey!)
P R O BAB I L I TY AN D STATI STI CS
FOR THE PORTFOLIO
Individual students or small groups can pursue this
longer-term project.
Does being left-handed give you some advantage in
playing baseball, similar to being tall in playing
basketball? Interested students might use a
reference book of baseball statistics to take a sample
of 100 or so professional baseball players (excluding
pitchers) who have been active within the last 10
years. What percentage of them have been lefthanded? Right-handed? (A circle graph would be a
good way to display this information.) How did the
average batting average for right-handed hitters
compare with the average batting average of lefthanded hitters?
Ste
am
er
Mc
Gu
rdy
What’s a
batting average?
Here’s the tricky part:
As part of the report, students will have to
explain carefully how they computed an
average batting average. The batting average of
a ballplayer who has had 1000 times at bat
should be given more weight than the average
of a player who has had only 100 at-bats.
Suppose a player has 250 hits in 1000 at-bats.
His batting average is .250. Suppose another
player has 35 hits in 100 at-bats. His batting
average is .350. Together, they have 285 hits
in 1100 at bats, so their combined average is
only .259. That’s much lower than .300,
which would be the average of the
averages.
It’s the number
of hits you got divided
by the number of
at-bats you had.
Math Talk
PROBABILITY
AND
STATISTICS
CONNECTIONS
The Perils of Polling:
Conducting Surveys
Choosing a
sample for
a survey
The Data Game:
Using Graphs
Using circle
graphs
31
Who, me?
80
10
20
70
90
0
100
30
40
WHOM DO YOU ASK? UNDERSTANDING SURVEYS
MathTalk
NAME
60
50
32
©1995 Children’s Television Workshop