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 zero and one (inclusive). List them in
[link] . Round the numbers to four decimal places or set the calculator MODE to four places.
Complete the table.
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Calculate the following:
$\overline{x}=$ _______
s = _______
first quartile = _______
third quartile = _______
median = _______
Organize the data
Construct a histogram of the empirical data. Make eight bars.
Construct a histogram of the empirical data. Make five bars.
Describe the data
In two to three complete sentences, describe the shape of each graph. (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, and so on. One way to help you determine a shape is to draw a smooth curve roughly through the top of the bars.)
Describe how changing the number of bars might change the shape.
Theoretical distribution
In words,
X = _____________________________________.
The theoretical distribution of
X is
X ~
U (0,1).
In theory, based upon the distribution
X ~
U (0,1), complete the following.
μ = ______
σ = ______
first quartile = ______
third quartile = ______
median = __________
Are the empirical values (the data) in the section titled
Collect the Data close to the corresponding theoretical values? Why or why not?
Plot the data
Construct a box plot of the data. Be sure to use a ruler to scale accurately and draw straight edges.
Do you notice any potential outliers? If so, which values are they? Either way, justify your answer numerically. (Recall that any DATA that are less than
Q_{1} – 1.5(
IQR ) or more than
Q_{3} + 1.5(
IQR ) are potential outliers.
IQR means interquartile range.)
Compare the data
For each of the following parts, 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: _______
first quartile: _______
median: _______
third quartile: _______
maximum value: _______
width of
IQR : _______
overall shape: _______
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
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
can someone help me with some logarithmic and exponential equations.
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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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