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Central limit theorem (pocket change)

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.
    Blank graph template. The horizontal axis is labeled Value of the change and the vertical axis is labeled Frequency.
  4. Calculate the following ( n = 1; surveying one person at a time):
    1. 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.
    This is a blank graph template. The horizontal axis is labeled Value of the change and the vertical axis is labeled Frequency.
  4. Calculate the following ( n = 2; surveying two people at a time):
    1. 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.
    This is a blank graph template. The horizontal axis is labeled Value of the change and the vertical axis is labeled Frequency.
  4. Calculate the following ( n = 5; surveying five people at a time):
    1. 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? X ¯ ~ _____(_____,_____)
  4. In one to two complete sentences, explain any differences in your answers to the previous two questions.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
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
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Introduction to statistics i - stat 213 - university of calgary - ver2015revb. OpenStax CNX. Oct 21, 2015 Download for free at http://legacy.cnx.org/content/col11874/1.3
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