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On Descriptive Statistical - Case Study Example

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The purpose of this paper is to find out the extent of elementary education level prevailing in different states of the US economy as per the statistics of 2004. it has often been claimed that the spread of education is very partial among the various states of the nation. This…
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Case Study on Descriptive Statistical
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wise Variation in the level of elementary education in USA. Table of Contents 3 Introduction 4 Data Source and Methodology 4 Results and Analysis 5
Conclusion 6
Bibliography 7
Appendix 8
Abstract
The purpose of this paper is to find out the extent of elementary education level prevailing in different states of the US economy as per the statistics of 2004. it has often been claimed that the spread of education is very partial among the various states of the nation. This paper aims to find empirical evidence to investigate the truthfulness of such a claim. Various statistical tools like standard deviation and coefficient of variation have been used in the paper to establish the same.

Introduction
In order to find the spread of minimum or elementary education in various states of the US economy, it is important to find out how far the given observations are scattered around the mean observation for which the standard deviation is used as a reliable measure. For the same reason, this paper has also taken the support of a histogram. The purpose of a histogram is to find out the frequency density, i.e., how the observations are clustered within the different classes.
Data Source and Methodology
The data for the number of students enrolled in US public elementary schools is obtained from the 2004 report published by the US National Center for Education. This data has been used to find out the spread of elementary education among various states in the US economy. But, before progressing it is important to define some useful statistics that will help to draw empirical conclusions.
The degree of scatteredness is measured be the standard deviation; but before defining it, it is necessary to calculate the mean of the observations, because, the scatteredness of observations actually suggests how far they are dispersed about their mean value. Now, mean is defined as,
X* = (∑Xi) / N where Xi = ith observation of the variable X, where i = 1, 2 … N.
After the mean value has been obtained, the standard deviation as a measure of dispersion could be found using the following formula,
SD = σ = √ ∑(Xi – X*)2 / N
Besides, the coefficient of variation for the concerned data is also being calculated since it will help in finding out the percentage of variations present in the data being collected. Coefficient of variation is defined as,
C.V. = (SD / Mean) x 100
All these statistics are being calculated in MS-Excel for the data being provided by the source given above.

Results and Analysis
The standard deviation statistic so obtained implies that the observations are rather too highly scattered about their mean value (670.2). This fact is prominent from the value of the coefficient of variation which indicates that the observations are scattered by a degree of 120% around their mean value.
The histogram derived from the data show that most of the observations are scattered towards the leftmost position in the graph, thus yielding a positively skewed curve. From the curve, however, one obvious point is that very few states have a high number of students enrolled in public elementary schools.
Conclusion
The purpose of this paper was to find out the spread of elementary education in the states of USA according to the 2004 statistics. The empirical data reveal that the observations indeed are highly scattered thus suggesting high levels of variations in the degree of elementary education among the various states in the USA.
However, one drawback of the study is that, the data for one particular year cannot conclude anything about the inherent behavior of a variable, especially when the possibility of externalities cannot be ruled out. Hence, a time-series analysis could have been a more relevant study in this regard.
Bibliography
U.S. National Center for Education Statistics, Digest of Education Statistics, 2009, “Public Elementary and Secondary School Enrollment by State”. Available at http://www.census.gov/compendia/statab/cats/education/elementary_and_secondary_education_schools_and_enrollment.html [Accessed on September 16, 2009].
Appendix
Data for the Number of Enrolments in the US Elementary Public Schools in 2004 (in ‘000).
1
Alabama
521.76
27
Montana
98.67
2
Alaska
91.98
28
Nebraska
194.82
3
Arizona
722.21
29
Nevada
288.75
4
Arkansas
328.19
30
New Hampshire
140.24
5
California
4507.92
31
New Jersey
975.99
6
Colorado
540.70
32
New Mexico
227.90
7
Connecticut
404.17
33
New York
1942.96
8
Delaware
83.60
34
North Carolina
985.74
9
District of Columbia
57.11
35
North Dakota
67.12
10
Florida
1857.80
36
Ohio
1267.09
11
Georgia
1118.38
37
Oklahoma
452.95
12
Hawaii
128.79
38
Oregon
376.81
13
Idaho
178.22
39
Pennsylvania
1234.83
14
Illinois
1483.65
40
Rhode Island
107.04
15
Indiana
720.01
41
South Carolina
504.26
16
Iowa
324.17
42
South Dakota
83.89
17
Kansas
321.26
43
Tennessee
670.88
18
Kentucky
485.80
44
Texas
3184.24
19
Louisiana
533.75
45
Utah
355.45
20
Maine
136.28
46
Vermont
65.94
21
Maryland
597.42
47
Virginia
839.69
22
Massachusetts
682.18
48
Washington
695.41
23
Michigan
1211.44
49
West Virginia
197.56
24
Minnesota
558.45
50
Wisconsin
577.95
25
Mississippi
361.09
51
Wyoming
57.29
26
Missouri
628.67

Results
Descriptive Statistics for the above data.
Histogram Read More
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