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Learning Math Home
Data Measurement and Variation
 
Session 1 Part A Part B Part C Part D Homework
 
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Session 1 Materials:
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B C D
Homework

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Solutions for Session 1, Homework

See solutions for Problems: H1 | H2 | H3


Problem H1

a. 

One question might be, "What is the average length of a pine needle from a fully grown pine tree?"

b. 

Here are some possible sources of the variation in this data:

 

Pine needles are inherently different and come in different sizes.

 

Measurement errors may have occurred.

 

The needles may have come from different places on the tree, which could affect their lengths.

 

The needles may have come from different trees, whose different locations could affect the needles' lengths.

 

Some of the needles may have come from one type of pine tree and some from another.

c. 

They probably will not all be identical, due to the many possible sources of variation.

<< back to Problem H1


 

Problem H2

a. 

Here are some possible sources of the variation in this data:

 

Coins are minted in different places.

 

Measurement errors may have occurred, including recording errors of the mint location.

 

These coins were obtained from different locations, some with more of a certain type of coin. For example, on the East Coast, you're more likely to see nickels with a P marking.

b. 

This variation is due to the fact that the same mints produce many different coins each year, and they all remain in circulation.

c. 

The location D appears most frequently; roughly half the data (51 coins out of 100) come from this location. The 1990s is the most frequently appearing decade, with 40 coins; the 1980s is a close second, with 37.

d. 

The coins with no mint location were minted between 1972 and 1978. One new question might be, "Where were the coins with no mint location minted?"

e. 

The data should be roughly comparable but not identical, due to variation. Some causes of this variation are the location in which the coins were obtained, the condition of the coins that are kept in circulation, and measurement error.

f. 

It seems clear that the coins with no mint location were minted in Philadelphia. The range of dates for the N coins is 1972-1978, and the earliest date for a P coin is 1981. In contrast, there are many coins from Denver minted through the 1970s. The implication is that Philadelphia didn't begin imprinting its location until after 1978. (There are not enough coins with the S mint mark to suggest that the larger number of coins with no mint location came from San Francisco.)

<< back to Problem H2


 

Problem H3

a. 

The measurements are very unlikely to be the same. Here are some possible sources of the variation in this data:

 

Measurement errors may have occurred.

 

The measurements are taken at different times of the day, which affects pulse rate.

 

The measurements are taken under different conditions, for example, at different levels of physical activity or stress.

b. 

This is difficult, since there is a lot of variation in pulse-rate data. You might take a large number of readings, then partition them into activities (working out, sleeping, eating, etc.) to find a typical pulse rate for each activity. Any single number to estimate overall pulse rate would be subject to a lot of variation, and any range that contains all possible pulse rates for one day would be a very wide one.

<< back to Problem H3


 

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