Research 2 - Descriptive Analysis
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Dec 6, 2023
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DESCRIPTIVE ANALYSIS
Helms School of Government, Liberty University.
PADM 702: Advanced Public Administration, Finance, and Budgeting
Professor: Leona R. Monroe, Ph.D., CDFM, DFMC3.
September 2023.
Author Note
I have no known conflict of interest to disclose.
Correspondence concerning this article should be addressed to:
Email: @libe
r
ty.edu
DESCRIPTIVE ANALYSIS
1
To
: Leona R. Monroe, Ph.D., CDFM, DFMC3.
From
: Subject
: Descriptive Analysis.
MEAN
In mathematics and/ or statistics, the mean is the average of a set of values. To calculate the
mean of a set of numbers, you add all the numbers in a data set and divide by the number of
values in the set (Almond, 2023).
For this analysis and with the help of Microsoft Excel, I individually computed (added) "State A"
and "State B's" "total monthly income and sales taxes" from January 1982 through July 1990. I
then divided each of those four categories of data by 102 (the total number of months taxes were
generated for each four category). The following "Means" were obtained from the descriptive
statistics I ran in Microsoft Excel:
STANDARD DEVIATION
Standard deviation is a statistical measure of how spread out a set of values is in relation to the
mean. It tells you how far each value is from the mean on average. A low standard deviation
means the values are close to the mean, while a high standard deviation means the values are
spread out (NLM, 2023).
Because I analyzed these data collectively with the Data Analysis tool of Microsoft Excel, I was
able to automatically generate the standard deviation for
"State A" and "State B's" "total monthly
income and sales taxes" from January 1982 through July 1990. This analysis shows that the
standard deviation measured how less and more spread the monthly taxes are from the “Means.”
The following "Standard Deviations" were obtained from the data I analyzed in Microsoft Excel:
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COEFFICIENT OF VARIATION
The coefficient of variation (CV) is a statistical measure of the dispersion of data points around
the mean. It is the ratio of the standard deviation to the mean. The CV is often expressed as a
percentage (Insee, 2023).
For this research, the coefficient of variation (CV) helped me analyze and compare the results
obtained from STATE A and B's monthly income and sales tax collection from January 1982
through July 1990
.
Since the data I analyzed came from two different data sets, State A and State B (with different
means), I could only compare the data using the Coefficient of Variation. To compute the
Coefficient of Variation, I divided all the "Standard Deviations" I had early obtained by their
corresponding "Mean" (standard deviation/ mean).
Calculations for State A’s Income and Sales tax:
1.
CV for “State A’s” income tax = SD of “State A’s” income tax SD
X 100
Mean of “State’s A” income tax
= $18,606,658
X 100
$42,178,465
CV = 44.11% or 0.4411
2.
CV for “State A’s” sales tax = SD of “State A’s” sales tax SD
X 100
Mean of “State’s A” sales tax
= $9,978,764
X 100
$33,385,142
CV = 29.89% or 0.2989
Calculations for State B’s Income and Sales tax:
1.
CV for “State B’s” income tax = SD of “State B’s” income tax SD
X 100
Mean of “State’s B” income tax
= $28,504,360
X 100
$84,459,073
CV = 33.75% or 0.3375
2.
CV for “State B’s” sales tax = SD of “State B’s” sales tax SD
X 100
Mean of “State’s B” sales tax
= $13,667,029
X 100
$66,281,496
CV = 20.62% or 0.2062
TABLE 1: DESCRIPTIVE STATISTICS FOR MONTHLY TAX COLLECTION FOR
STATE A
TABLE 2: DESCRIPTIVE STATISTICS FOR MONTHLY TAX COLLECTION FOR
“STATE B”
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TABLE 3: MEAN AND STANDARD DEVIATION AND COMPARISON BETWEEN
"STATE A" AND "STATE B"
INTERPRETING THE COEFFICIENT OF VARIATION
If a Coefficient of Variation equals one or 100%, it simply means that the standard deviation
equals the mean. Values less than one indicate that the standard deviation is smaller than the
mean (typical), while values greater than one occur when the standard deviation is greater than
the mean (Frost, 2023). Coefficient of Variations of 5% or less are generally considered good.
The Coefficient of Variations of 10% and higher is considered bad (Madelon, 1999).
In conclusion, the data and/ or analysis above shows the following:
1.
Which set of data shows the highest variation? The data and/ or analysis above shows that
“State A” Total Income Taxes has the highest variation because its coefficient of variation
is 44.11% or 0.4411
2.
Which set of data shows the lowest variation? The data and/ or analysis above shows that
“State B” Total Sales Taxes has the lowest variation because its coefficient of variation
is 20.62% or 0.2062
3.
Which state shows the highest and lowest variations in total income and total sales tax
collections? The data and/ or analysis above shows that “State A” has a higher variation
for its total income and sales taxes while “State B” has a lower variation for its total
income and sales taxes.
4.
Which state’s tax collections are more consistent and fluctuate the least? The data and/ or
analysis above shows that “State B” tax collections are more consistent and fluctuate the
least because the general rule of thumb for Coefficient of Variation is that the lower the
Coefficient of Variation, the smaller the variability.
REFERENCE
Almond, N. (2023). "
W
hat Are Mean, Median and Mode?” https://thirdspacelearning.com/us/blog/what-is-mean-median-mode/#:~:text=The
%20mean%20is%20adding%20up,as%20a%20list%20of%20numbers
.
Frost, J. (2023). "
Coefficient of Variation.
" https://statisticsbyjim.com/basics/coefficient-
variation/
Insee (2023). "
Coefficient of Variation.
" https://www.insee.fr/en/metadonnees/definition/c1366#:~:text=The%20coefficient%20of
%20variation%20(CV,generally%20expressed%20as%20a%20percentage
.
Madelon, F. Z. (1999). "Mean, Standard Deviation, and Coefficient of Variation.
" https://www.westgard.com/lesson34.htm#:~:text=CVs%20of%205%25%20or
%20less,the%20CV%20may%20be%20low
.
NLM (2023). "
Standard Deviation.
" https://www.nlm.nih.gov/oet/ed/stats/02-
900.html#:~:text=A%20standard%20deviation%20(or%20%CF%83,data%20are
%20more%20spread%20out
.
Stephanie G.
(2023).
"
How to Find a Coefficient of Variation.
" https://www.statisticshowto.com/probability-and-statistics/how-to-find-a-coefficient-of-
variation/
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