Background InformationThe Central Limit Theorem is similar to the Law of Large Numbers. The more samples we take from ou

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Background InformationThe Central Limit Theorem is similar to
the Law of Large Numbers. The more samples we take from our sample
or the population, the closer our sample resembles a Normal
Distribution. When we look at means of samples, it happens even
more quickly! In this lab we are looking at 30 values at a time.
While the data is being pulled from a larger set, this
randomization for the initial set allows for a better change in
situation each time. The data you will be using is randomized from
90 values.The sets are:Set C1A random set of 30 individual data
values from the original list of 197 values.Set C5A random set of
30 means of groups of 5 data values from the original list of 197
values. (i.e. The mean is calculated for a set of 5 randomly
selected data values. This is repeated 30 times and those means
become your list.)Set C20Random set of 30 means of groups of 20
data values from the original list of 197 values. (i.e. The mean is
calculated for a set of 20 randomly selected data values. This is
repeated 30 times and those means become your list.)
InstructionsThe Desmos site below is set up to do all the
randomization and calculations for you. Turn off and on the
different graphs as needed to see what is happening and to take the
individual screenshots for each
set.https://www.desmos.com/calculator/oyvo0cokstClick the crossed
lines button at the top left a few times to see how the histogram,
mean, and standard deviation change with each randomization, size,
and type of sample. You can also change colors with the gear
icon.After you have done this a few times, copy the link to your
individualized set of dataWhat is the link to your work in Desmos?
(Use the button that looks like this: , not the web address)On the
next page, insert an image of each of the individual histograms,
with the values for the corresponding means and standard
deviations, below so it is easier to discuss. Make sure to show one
and only one histogram per exported image.To export an image of
your histogram, follow these instructions. HistogramMeanStandard
DeviationSet C1HistogramMeanStandard DeviationSet
C5HistogramMeanStandard DeviationSet C20 Discussion Questions:(For
each one, useone to two complete sentences to explain what
happened.)How did the shape of the distribution of the data change,
as size of the averaged set changed?How did the mean change, as
size of the averaged set changed?How did the standard deviation
change, as size of the averaged set changed?