# 5.9 Lab: continuous distribution

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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:

Names:

## 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:
• $\overline{x}=$
• $s=$
• 1st quartile =
• 3rd quartile =
• Median =

## Organize the data

1. Construct a histogram of the empirical data. Make 8 bars.
2. Construct a histogram of the empirical data. Make 5 bars.

## 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 $X$ ~ $U\left(0,1\right)$ . Use it for this part.
3. In theory, based upon the distribution $X$ ~ $U\left(0,1\right)$ , complete the following.
• $\mu =$
• $\sigma =$
• 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?

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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da
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I only see partial conversation and what's the question here!
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yes that's correct
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I think
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nanocopper obvius
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LITNING
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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 .
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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what is Nano technology ?
write examples of Nano molecule?
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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
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Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
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yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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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