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In this lab exercise, students will compare and contrast empirical data from a random number generator with the Uniform Distribution.

Class Time:


Student learning outcomes:

  • The student will compare and contrast empirical data from a random number generator with the Uniform Distribution.

Collect the data

Use a random number generator to generate 50 values between 0 and 1 (inclusive). List them below. Round the numbers to 4 decimal places or set the calculator MODE to 4 places.

  1. Complete the table:
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
  2. Calculate the following:
    • x ¯ = size 12{ {overline {x}} ={}} {}
    • s = size 12{s={}} {}
    • 1st quartile =
    • 3rd quartile =
    • Median =

Organize the data

  1. Construct a histogram of the empirical data. Make 8 bars.
    Blank graph with relative frequency on the vertical axis and X on the horizontal axis.
  2. Construct a histogram of the empirical data. Make 5 bars.
    Blank graph with relative frequency on the vertical axis and X on the horizontal axis.

Describe the data

  1. Describe the shape of each graph. Use 2 – 3 complete sentences. (Keep it simple. Does the graph go straight across, does it have a V shape, does it have a hump in the middle or at either end,etc.? One way to help you determine a shape, is to roughly draw a smooth curve through the top of the bars.)
  2. Describe how changing the number of bars might change the shape.

Theoretical distribution

  1. In words, X =
  2. The theoretical distribution of X is X ~ U ( 0 , 1 ) . Use it for this part.
  3. In theory, based upon the distribution X ~ U ( 0 , 1 ) , complete the following.
    • μ =
    • σ =
    • 1st quartile =
    • 3rd quartile =
    • median = __________
  4. Are the empirical values (the data) in the section titled "Collect the Data" close to the corresponding theoretical values above? Why or why not?

Plot the data

  1. Construct a box plot of the data. Be sure to use a ruler to scale accurately and draw straight edges.
  2. Do you notice any potential outliers? If so, which values are they? Either way, numerically justify your answer. (Recall that any DATA are less than Q1 – 1.5*IQR or more than Q3 +1.5*IQR are potential outliers. IQR means interquartile range.)

Compare the data

  1. For each part below, use a complete sentence to comment on how the value obtained from the data compares to the theoretical value you expected from the distribution in the section titled "Theoretical Distribution."
    • minimum value:
    • 1st quartile:
    • median:
    • third quartile:
    • maximum value:
    • width of IQR:
    • overall shape:
  2. Based on your comments in the section titled "Collect the Data", how does the box plot fit or not fit what you would expect of the distribution in the section titled "Theoretical Distribution?"

Discussion question

  1. Suppose that the number of values generated was 500, not 50. How would that affect what you would expect the empirical data to be and the shape of its graph to look like?

Questions & Answers

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.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Nerisha Reply

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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