# 8.4 Central limit theorem (pocket change)

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Class Time:

Names:

## Student learning outcomes

• The student will demonstrate and compare properties of the central limit theorem.

## Note

This lab works best when sampling from several classes and combining data.

## Collect the data

1. Count the change in your pocket. (Do not include bills.)
2. Randomly survey 30 classmates. Record the values of the change in [link] .
 __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________
3. Construct a histogram. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.
4. Calculate the following ( n = 1; surveying one person at a time):
1. $\overline{x}$ = _______
2. s = _______
5. Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.

## Collecting averages of pairs

Repeat steps one through five of the section Collect the Data. with one exception. Instead of recording the change of 30 classmates, record the average change of 30 pairs.

1. Randomly survey 30 pairs of classmates.
2. Record the values of the average of their change in [link] .
 __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________
3. Construct a histogram. Scale the axes using the same scaling you used for the section titled Collect the Data . Sketch the graph using a ruler and a pencil.
4. Calculate the following ( n = 2; surveying two people at a time):
1. $\overline{x}$ = _______
2. s = _______
5. Draw a smooth curve through tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.

## Collecting averages of groups of five

Repeat steps one through five (of the section titled Collect the Data ) with one exception. Instead of recording the change of 30 classmates, record the average change of 30 groups of five.

1. Randomly survey 30 groups of five classmates.
2. Record the values of the average of their change.
 __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________
3. Construct a histogram. Scale the axes using the same scaling you used for the section titled Collect the Data . Sketch the graph using a ruler and a pencil.
4. Calculate the following ( n = 5; surveying five people at a time):
1. $\overline{x}$ = _______
2. s = _______
5. Draw a smooth curve through tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.

## Discussion questions

1. Why did the shape of the distribution of the data change, as n changed? Use one to two complete sentences to explain what happened.
2. In the section titled Collect the Data , what was the approximate distribution of the data? X ~ _____(_____,_____)
3. In the section titled Collecting Averages of Groups of Five , what was the approximate distribution of the averages? $\overline{X}$ ~ _____(_____,_____)
4. In one to two complete sentences, explain any differences in your answers to the previous two questions.

where we get a research paper on Nano chemistry....?
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There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
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yes that's correct
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I think
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brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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what school?
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biomolecules are e building blocks of every organics and inorganic materials.
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how did you get the value of 2000N.What calculations are needed to arrive at it
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