Reporting on Results of
Analysis
Name
Institutional
Affiliation
Reporting
on Results of Analysis
Statistics are divided into inferential and descriptive
statistical techniques. The two branches attain different objectives, and each serves a specific purpose. However, the two analytical techniques are
used concurrently for proper data understanding and interpretation. Descriptive
statistical method deals with how data is presented and collected while the inferential statistical technique involves making appropriate conclusions based on
statistical analysis of descriptive statistics. Therefore, one statistical technique cannot exist without the other. The
concept of inferential and descriptive statistical techniques is highly applied
in businesses for problem-solving and decision making.
For instance, companies apply
statistical techniques when they face
situations that require the selection of the
best solution among alternatives. Additionally,
statistical methods are used to identify and compare relationships among variables
that influence decision making. This paper intends to report the results of descriptive and inferential
statistical techniques. The paper examines migration data of Mississippi
and California states to find where the headquarters of a moving company will
be located. The descriptive technique has
analyzed the two states using mean, percent, variance, percentile ranks, and
standard deviation while the inferential
technique has done it using simple linear regression. Also, the paper has
identified the cautions, limitations, and generalizations experienced during
the analysis. Additionally, the paper has come up with a conclusion based on
the results of analyzing the two states. The results reveal that the moving
company should locate its headquarters in
California.
An Analysis of the
Business Question
The executive
leaders of a U.S founded company are trying to determine a state that has
significant business potential in which to locate its headquarters. The major income for a moving company is transportation fees charged from customers.
Thus, a change in migration rate impacts the bottom line. However, high migration
rate can affect the revenue either favorably or adversely. The current state of
residence for the moving company, Mississippi, has been adversely affecting incomes due to limited movement of residents.
If the company was operating in a state with a large
population where people constantly move in and out of surrounding towns, it would
thrive. As a result, the company would generate more income and mitigate the
vulnerability to the going concern. The company’s executives are concerned
about the performance of the company and have addressed the issue of
establishing the headquarters of the company to another state. Thus,
inferential and descriptive statistics will be essential to provide an analytical basis for comparison of the current
state (Mississippi) and the state to relocate (California) to determine the
best state.
California has been
selected as the analytic state due to its higher domestic migration rate
compared to Mississippi. According to Economic Research Service (2017),
California had a net migration of 5.9% for the years 2010 to 2017 while
Mississippi had a net of 0.5 % during the same period. Moreover, California has
a large geographical area of 423,970 km²
and a population of 39.54 million by the year 2017 while Mississippi’s
geographic area is 125,433 km² with a
population of 2.984 during the same period (Economic Research
Service, 2017). However, the
business problem will be solved by
analyzing the two states based on quantitative statistics.
Data
Analysis Techniques and Methods
The
methods selected to analyze the data are inferential and descriptive data
analysis. Inferential data analysis is used to draw conclusions that are beyond
individual data. Inferential statistics enable the analyst
to make predictions using data
(Seth, 2018). Moreover, the statistics involve the use of samples to make generalizations about a
population. The inferential analysis technique is appropriate for the analysis
because it is impractical to calculate how often people in Mississippi and
California states relocate. Thus, the method
will facilitate sampling which saves time and money (Bowerman, O'Connell, &
Murphree, 2017). For example, the technique is used in hospital
laboratories whereby patient blood samples are
taken for examination.
Descriptive
analysis assists in describing and
understanding the features of particular data by giving its measures and a summary. Descriptive statistics are measures of
variability or central tendency that use tables, general discussions, and
graphs to find the meaning of the analyzed
data. Descriptive analysis is appropriate for the study because it will help in saving time and improve understanding
of the data by the use of summaries. For
instance, the net migration means
for California and Mississippi are represented
in a table which is easy to understand and interpret.
Descriptive Statistical
Analysis
The analysis
comprises of five descriptive statistical
techniques that include mean, percent, variance, percentile ranks, and standard
deviation. According to Seth
(2018),
mean is a measure of a tendency that locates
distribution by various points and is used
when indicating an average. Therefore, the mean of the net and domestic
migration for Mississippi and California states will be calculated to show the average number of people moving in out
of the two states. The state with the lowest mean of net migration for
the period from 2010 to 2017 will be more favorable. Negative net migration mean for the two states indicates the migration rate is higher in 2017 than it was in the year 2010. Also, the
domestic mean for the two populations is calculated
and compared with the net migration mean. A state with a higher domestic mean and a lower net migration mean indicate a continued rising of the
migration rate. Table 1 represents migration data of Mississippi and California
used to compare the two states. The mean of the two companies are as follows
based on based on data from appendix A.
Mean
Formula
Where ΣXi - total net migration for
California
ΣXi -total net
migration for Mississippi
μ - mean
N - Number of years
California
Mississippi
Variance and standard deviation measure dispersion that identifies the
spread of scores by stating intervals. The measures are used when studying ‘spread out’ data. The measures give a signal when the data is spread out at a high level such that it
affects the mean. Variance and standard deviation are used together due to
their close relationship. According to Holcomb (2016), standard deviation or
variance is equal to the difference between mean and observed score. The
standard deviation helps the business analyst to determine whether net migration
rates for California and Mississippi points divert from the mean. A higher
standard deviation or variance shows that the net migration rate is spread out to the extent of affecting the mean as shown in
the calculations below. However, a variance zero means that the migration is
equal to the mean. The variance and standard deviation of the Mississippi and
California net migration for the period 2010 to 2017 is represented below
Variance
Standard
Deviation
California
Mississippi
Similar to
frequency, percent measures how often something occurs. The measure of a percent in the analysis is used to indicate how
often people move in and out of Mississippi and California. The state with a high percentage
of net migration shows potential in significant business while a low percent
reveals suppressed business operations. Appendix C table shows the different percentages used to analyze the two
states.
Percentile
ranks are a measure of the position that
describes how scores fall about one
another. The percentiles rely on standardized scores and are used to compare
scores to a normalized score (Holcomb, 2016). The percentile will be used in
the analysis to indicate how the normal
net migration rate in California and Mississippi relates to the present rates. A percentile rank higher than the net
migration rate reveals that people had
decreased the movements while a percentile rank lower than the present net migration rate indicates a rapid
rise in the net migration rate. The percentile ranks for California and
Mississippi are to be compared the one
with a high positive rank preferred. California has a normal annual net migration of 79422.5 and
Mississippi 5098.13. However, in 2017 there was a net migration of 170000 for
California and 8000 for Mississippi. Thus, California has a higher net
migration rate.
Inferential
Statistical Analysis
The
inferential technique used to make a prediction
is simple linear regression analysis. The technique
examines the relationship between net migration rate and years in California
and Mississippi states using a straight line chart. According to Sahu, Pal &
Das (2015), simple linear regression analysis uses two-dimensional sample points, a dependent and independent variable; thus it is appropriate
for the analysis. The values of the dependent
variable are accurately predicted as
functions of the independent variable. The variables for the analysis include
duration in years from 2010 to 2017 and net migration rate. Simple linear
regression is used in the analysis to
predict the net migration rates using the two variables. Simple linear
regression analysis is also highly used in business for pricing, promotions and
marketing effectiveness. Sahu et al. (2015) noted that a linear equation is
used by companies to confirm that money invested in marketing a particular
product yields a guaranteed return on
investment. Table 3 in the appendices represents the
net migration rates for California and Mississippi for the period 2010 to 2017.
The data has been used to analyze simple linear regressions of the states.
Where X –net migration
Y – Years
N -8
b- Slope
a - Intercept
Formula
Y = a + bX
California
Thus, 
Mississippi
Thus, 
Assumptions
The
Descriptive statistics hold the assumption that variables used in the analysis
including population and duration in years for California and Mississippi are
normally distributed. The normality is confirmed by the skew and Kurtosis which
is similar to the differences in net migration means of the two states (Meuleman,
Loosveldt, & Emonds, 2015). Also, the linearity assumption is held by the
analysis due to the linear relationship between net migration and years for
California and Mississippi. The linearity assumption is assessed by linear
regression that shows an increase in net migration in California as the year's
increases.
Results
The
statistical data analysis created for mean indicated that California had a
higher mean than Mississippi. Also, the percent indicates that the net
migration percentages of California have been increasing compared to
Mississippi. The research further shows that Californian’s net migration
variance is 2, 155,936,209 and Mississippi’s 11,764,378 (Cox, 2017; Governing.com, 2019). Thus, California’s
net migration data was more spread out
than Mississippi’s. Also, the analysis indicated that the standard deviation
for California was 46,432 and that of Mississippi 3,430. The data reveals that the mean is not much
affected although California has a higher value by 43,002. California has a normal annual net migration of 79,422.5 and
Mississippi 5098.13. However, in 2017 there was a net migration of 170,000 for
California and 8,000 for Mississippi (Governing.com,
2019). Thus, California has a higher net migration rate with 9,422.5 compared
to Mississippi’s 2,901.87. Moreover, the
analysis found that the simple linear
regression line for California reveals an upward movement than Mississippi’s.
Conclusion
The
paper aimed at using inferential and descriptive statistical techniques to make
decisions on the state that the moving company should locate its headquarters. The
study shows that techniques play a significant role in analyzing statistical data.
The two statistical tools are commonly used due to their accuracy, use of
verified data and free from human bias. Net migration data was analyzed using
five different measures created based on the descriptive statistical
techniques. All the techniques created were
in favor of the California State by predicting a high and positive net
migration rate in the future. Also, the
linear regression analysis graphically showed a rising trend for the California
net migration rates. Therefore, it is evident that California is the best state
that has significant business potential due to the high net migration rate.
Cautions and limitations
Although
statistics make unbiased conclusions, it has cautions and limitations.
Therefore, analysts are supposed to use every technique with care because each
has a purpose and objective to attain.
For instance, mean is only supposed to be a measure of central tendency
while percentile rank is specifically designed to be a measure position. A mixture of the two would give inappropriate
results. The mean is calculated for numerical data, but
it does not always give a meaningful value. Besides, a mean is affected by skewed distributions and outliers.
Also, the simple linear regression analysis assumes a linear relationship
between the dependent and independent variable. However, that is not always the
case. In a specific circumstance, it is
usually incorrect to assume the linear relationship because some relationships
are curved.
Generalizations
For
a perfect analysis, there is an assumption that the exact number of people
moving in and out of California and Mississippi are known. However, that is not the case because of the existence of illegal immigrants as well as
those who not involved in the surveys. Also, there are always human errors in
calculating and submitting the data. Additionally, there are many approaches to
a problem. For instance, variation is found by standard deviation and mean
deviation which yields different results.
Therefore, it should not be assumed that
statistics is the only method to use in research.
References
Bowerman,
B., O'Connell, R., & Murphree, E. (2017). Business statistics in
practice: Using data, modeling, and analytics (8th ed.). New York, NY:
McGraw
Cox, W. (2017). The
Migration of Millions: 2017 State Population Estimates | Newgeography.com.
Retrieved from http://www.newgeography.com/content/005837-the-migration-millions-2017-state-population-estimates
Governing.com. (2019).
State Migration Rates, Net Totals: 2011-2016. Retrieved from
http://www.governing.com/gov-data/census/state-migration-rates-annual-net-migration-by-state.html
Holcomb, Z. C.
(2016). Fundamentals of descriptive statistics. Routledge.
Meuleman,
B., Loosveldt, G., & Emonds, V. (2015). Regression analysis: Assumptions
and diagnostics. The SAGE handbook of regression
Analysis and Causal Inference, 83-111.
Sahu, P. K., Pal, S. R., & Das, A. K. (2015). Estimation
and inferential statistics. New Delhi: Springer.
U.S. Department of Agriculture, Economic
Research Service. (2017). Download data: County-level data Sets. Retrieved from
https://www.ers.usda.gov/data-products/county-level-data-sets/county-level-data-sets-download-data/
Appendix
A
Net
Domestic Migration
|
Net
Domestic Migration
|
|
Year
|
California
(X1)
|
Mississippi
(X2)
|
|
|
|
2010
|
45,000
|
700
|
1,184,942,929
|
19,342,404
|
|
2011
|
50,000
|
1,300
|
865,712,929
|
14,424,804
|
|
2012
|
78,532
|
3,809
|
793,881
|
1,661,521
|
|
2013
|
70,149
|
2,160
|
86,007,076
|
8,631,944
|
|
2014
|
97,674
|
6,390
|
333,135,504
|
1,669,264
|
|
2015
|
70,495
|
10,959
|
79,709,184
|
34,351,321
|
|
2016
|
160,000
|
7,467
|
6,492,814,084
|
5,612,161
|
|
2017
|
170,000
|
8,000
|
8,204,374,084
|
8,421,604
|
|
Sum
|
ΣX1= 635,380
|
Σ X2= 40,785
|
17,247,489,671
|
94,115,023
|
Table 1
Sources: (Cox, 2017; Governing.com, 2019).
Appendix
B
Net
Domestic migration trend Graph
Appendix
C
Percentage
Analysis
|
Years
|
Percentage
Analysis
|
|
California
|
Mississippi
|
%
net migration
|
%
net migration
|
|
|
California
|
Mississippi
|
|
2010
|
45,000
|
700
|
6.07%
|
1.72%
|
|
2011
|
50,000
|
1,300
|
6.74%
|
3.19%
|
|
2012
|
78,532
|
3,809
|
10.59%
|
9.34%
|
|
2013
|
70,149
|
2,160
|
945.60%
|
5.30%
|
|
2014
|
97,674
|
6,390
|
1316.63%
|
15.67%
|
|
2015
|
70,495
|
10,959
|
9.50%
|
26.87%
|
|
2016
|
160,000
|
7,467
|
21.57%
|
18%
|
|
2017
|
170,000
|
8,000
|
22.92%
|
0.196151
|
|
741850
|
40785
|
|
|
Table 2
Sources: (Cox, 2017; Governing.com, 2019).
Appendix
D
Linear
regression analysis
|
Year
(y)
|
California
(X1)
|
Mississippi
(X2)
|
YX1
|
YX2
|
(X1)2
|
(X2)2
|
|
2010
|
45,000
|
700
|
45,000
|
700
|
2,025,000,000
|
490000
|
|
2011
|
50,000
|
1,300
|
100,000
|
2,600
|
2,500,000,000
|
1690000
|
|
2012
|
78,532
|
3,809
|
235,596
|
11,427
|
6,167,275,024
|
14508481
|
|
2013
|
70,149
|
2,160
|
70,145
|
8,640
|
4,920,882,201
|
4,665,600
|
|
2014
|
97,674
|
6,390
|
488,370
|
31,950
|
9,540,210,276
|
40,832,100
|
|
2015
|
70,495
|
10,959
|
422,970
|
65,754
|
4,969,545,025
|
120,099,681
|
|
2016
|
160,000
|
7,467
|
1,120,000
|
52,269
|
25,600,000,000
|
55,756,089
|
|
2017
|
170,000
|
8,000
|
1,360,000
|
64,000
|
28,900,000,000
|
64,000,000
|
|
Sum
|
ΣX1= 635,380
|
Σ X2= 40,785
|
3,842,081
|
237340
|
84,622,912,526
|
302,041,951
|
Table 3:
Sources: (Cox, 2017; Governing.com, 2019).
