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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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