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Government Budgeting Cycle: Advanced Public Administration Finance
Students
Institution
Course
Instructor
Date
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Given Data A and Data B
State A:
82,93,91,69,96,61,88,58,59,100,93,71,93,71,78,98
State A Calculations
Mean 81.21428571
Standard Error 4.045318243
Median 85
Mode 93
Standard Deviation 15.13619489
Calculating Mean
Mean=Score/ Count
Mean=1137/14=81.21428571
Calculating Standard Deviations
Standard Deviation=[(Score-Mean^2)/ Count-1]61/2
Follow these steps to calculate the standard deviation for the data of State A:
Sample data for State A: 82, 93, 91, 69, 96, 61, 88, 58, 59
Find the mean:
Sum up all the values = 82 + 93 + 91 + 69 + 96 + 61 + 88 + 58 + 59 + 100 + 93 + 71
+ 78 + 98 = 1137
Number of values = 14
The Average = 1137 / 14 = 81.21428571
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Subtract the mean from each data point and square the results:
(82 - 81.21428571)^2
(93 - 81.21428571)^2
(91 - 81.21428571)^2
(69 - 81.21428571)^2
(96 - 81.21428571)^2 = 218.8849
(61 - 81.21428571)
(88 - 81.21428571)^2 = 45.6224
(58 - 81.21428571)^
This equals 496.0449, or
(100 - 81.21428571)^2 = 352.0449
(93 - 81.21428571)^2
, and I already committed to pressing enter
(78 - 81.21428571)^2 = 10.6224
(98 - 81.21428571)^2
Calculate the sum of the squared differences:
0.6224 + 139.2449 + 96.0449 + 149.6224 + 218.8849 + 409.6224 + 45.6224 +
539.2449 + 496.0449 + 352.044
Sum up the squared differences and divide by (n - 1), where n is the number of data
points :
2983.6912 / (14 - 1 ) = 2983.
To get the standard deviation you have to calculate the square root of the above result:
√229.5145 = 15.13619489
Therefore, the standard deviation in the data set at State A is 15.13619489.
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Calculating Coefficient Variations
Coefficient Variations=Standard Deviation/ Mean
Standard deviation= 15.13619489
Mean=81.21428571
Coefficient variations=15.13619489/ 81.214285714
=0.1864
State B Calculations
Scores=1133
Count=14
Mean =scores/count
1133/14=80.92857143
Standard Deviation
B State: 83, 94, 90, 68, 95, 60, 87, 57,60,99,92,72,79,97
Find the average:
Sum of all values = 83 + 94 + 90 + 68 + 95 + 60 + 87 + 57 + 60 + 99 + 92 + 72 + 79
+ 97 = 1133
Number of values = 14
Mean = 1133 / 14 = 80.92857143
Calculate the difference of each data point from the average value and square the
differences:
(83 - 80. 92857143)^2
94 - 80. 92857143)^2
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(90 - 80.92857143)^2
(68 - 80.92857143)^2
(95 - 80.92857143)^2
(60 - 80. 92857143)^2
(87 - 80.92857143)^2 = 36.4489
(57 - 80. 92857143)^2
(60 - 80. 92857143)^2
Step 3. Now, subtract the average from
(92 - 8092857143)^2
(72 - 80. 92857143)^2
(79 - 80.92857143)^2
This is: (97 - 80.928
Sum the squared differences:
4.4489 + 169.4489 + 81.4489 + 164.4489 + 196.4489 + 441.4489 + 36.4489 +
576.4489 + 441.4489 + 324.448
Divide by the sum of squared differences by n - 1, where n is the number of data
points:
2900.2896 / (14 - 1) = 2900.2896 /
Take the square root of the variance to get the standard deviation: √223.0992 = 14.
Therefore, the hypothetical data set for State B has a standard deviation of about
15.07.
Calculating Coefficient Variations
Coefficient variations=15.07/80. 92857143
=0.1862
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Key Final Results
State A
Total Income Tax Total Sales Tax
Mean 81.214285714
Standard Deviations 15.07
Coefficient Variations 0.1862
State B
Mean 80. 92857143
Standard Deviations 15.13619489
Coefficient Variations 0.1864
Comparison:
The coefficients of Variation between State A and State B are very similar, reflecting
that their respective variability of data sets is quite close. This makes it easier to compare the
data from both states, even though they differ in the means and the standard deviations.
Conclusion:
From the calculation, we can surmise that the data for the two states have similar
levels of variation relative to their means. This comparison gives the reader a sense of the
relative dispersion of the values of both the income taxes and sales tax in both states.
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