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Session 1:
Homework

Problem H1

Solution  

We used a metric tape measure to measure the lengths of 20 pine needles to the nearest millimeter:

Length of Needles (in millimeters)

117

56

48

69

71

120

111

49

68

110

109

64

93

43

109

37

93

40

86

47


a. 

Think of a question that collecting this data might answer.

b. 

Notice that the 20 pine-needle measurements are not all the same. What is the source of this variation?

c. 

If you have access to some pine needles, measure the length (to the nearest millimeter) of 10 different needles with a metric ruler. If you do not have access to pine needles, measure the length (to the nearest millimeter) of 10 different pieces of spaghetti with a metric ruler. Are the lengths the same?


 

Problem H2

Solution  

Ask a question
Where were my nickels minted?
When were my nickels minted?

collect data
A nickel's mint location (if present) is located on the head side of the coin below Jefferson's ponytail. We recorded the mint locations and years for 100 nickels ("S" indicates San Francisco, "D" indicates Denver, "P" indicates Philadelphia, and "N" indicates that no mint location was present):

Loca-
tion

Year

P

1997

D

1989

D

1995

D

1986

P

1983

D

1993

N

1976

P

1989

D

1982

D

1989

D

1972

D

1996

P

1995

D

1998

N

1978

P

1991

D

1985

D

1987

D

1988

D

1983

 

Loca-
tion

Year

D

1972

P

1995

D

1998

D

1995

P

1991

N

1972

P

1996

P

1990

P

1989

D

1989

D

1971

D

1980

P

1996

P

1986

P

1986

N

1976

P

1985

D

1997

P

1984

P

1995

 

Loca-
tion

Year

P

1985

P

1988

N

1978

D

1988

D

1998

P

1990

D

1982

P

1998

P

1983

D

1973

D

1986

D

1987

D

1991

P

1990

N

1973

D

1982

P

1996

S

1970

P

1996

P

1991

 

Loca-
tion

Year

D

1994

P

1989

P

1997

P

1993

D

1986

N

1975

D

1990

D

1993

D

1983

P

1995

P

1986

S

1968

D

1995

N

1974

P

1990

D

1984

P

1997

P

1981

D

1976

P

1984

 

Loca-
tion

Year

N

1974

D

1976

D

1998

D

1985

D

1971

D

1996

D

1991

P

1986

D

1995

P

1982

S

1970

D

1975

D

1982

D

1991

P

1990

D

1973

D

1974

D

1997

D

1976

D

1981

 

a. 

There are differences in the mint locations. What is the source of this variation?

b. 

There are differences in the mint years. What is the source of this variation?

c. 

What observations can you make about this data? For example, which location appears most frequently? Which decade?

d. 

When were the coins with no mint location minted? Does this suggest any new statistical questions?

e. 

Record the mint locations and years for 10 of your own nickels. How do your data compare to the data recorded above?

f. 

(Optional) Suppose you knew that the coins with no given mint location were in fact minted in either Philadelphia, Denver, or San Francisco. Can you pinpoint where these coins were minted? Defend your answer, using the data in this problem.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
View the Session 2 video to see how the onscreen participants solved this problem.   Close Tip

 

Problem H3

Solution  

Ask a question
What is your pulse rate?

collect data
Take your pulse rate, in beats per minute, seven times during the same day.

a. 

Are the measurements of your pulse rate the same? If not, what is the source of this variation?

b. 

Suppose you wanted to estimate your typical pulse rate. How could you answer this statistical question?

Try this experiment on yourself. You might take your pulse rate under several different conditions, for example, early in the morning, late in the day, and after exercising. Are your measurements the same?


Suggested Readings:

Krus, David and Webb, James (Autumn, 1997). "Demonstrating Variance Using the Muller-Lyer Illusion." Teaching Statistics, 19 (3), 72-76.
This article first appeared in Teaching Statistics <http://science.ntu.ac.uk/rsscse/ts/> and is used with permission.

Download PDF File:
Demonstrating Variance Using the Muller-Lyer Illusion
Continued

Principles and Standards for School Mathematics. (Reston, VA: National Council of Teachers of Mathematics, 2000) Standards on Data Analysis and Probability by grade level: K-2, 108-115; 3-5, 176-181; and 6-8, 248-255.
Reproduced with permission from the publisher. Copyright © 2000 by the National Council of Teachers of Mathematics. All rights reserved.

Download PDF File:
Data Analysis and Probability Standards for Grades Pre-K-2
Continued


Data Analysis and Probability Standards for Grades 3-5
Continued


Data Analysis and Probability Standards for Grades 6-8
Continued


Next > Session 2: Data Organization and Representation

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