Analysis of Economic and Business Data using Statistical Methods

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Statistics for management
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Contents
INTRODUCTION:........................................................................................................3
LO1 INTERPRETATION OF THE ECONOMIC AND BUSINESS DATA....................4
LO2 ANALYSIS AND EVALUATION OF THE RAW BUSINESS DATA WITH THE
HELP OF THE STATISTICAL METHODS..................................................................8
LO3 APPLICATION OF THE STATISTICAL METHOD IN BUSINESS PLANNING. 12
LO4 COMMUNICATE THE FINDINGS WITH THE USE OF THE APPROPRIATE
CHARTS AND TABLES............................................................................................15
CONCLUSION.......................................................................................................... 18
REFERENCES..........................................................................................................19
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INTRODUCTION:
The aim of the unit is to help in establishing the understanding of how one can
enhance the decision making with the help of the statistical methods. In this
assignment usage of various statistical techniques are been implemented along with
their importance in taking the management related decisions including the way of
informing the management thinking. At the end of the unit there will be an
enhancement in the numerical solving ability along with the increase in the
confidence level concerning the data handling and also should learn to transform the
data into the knowledge and information.
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LO1 INTERPRETATION OF THE ECONOMIC AND BUSINESS DATA
The nature of the data
In this particular question, a study is been conducted using the random sample of
1000 participants each so as to compare the earnings of the men and women
working in the private and public sector. The data is been collected for the year 2009
to2016. The annual mean earnings for the above mentioned year is been taken
(Siegel, 2016). The data is collected on the ratio scale which has the following nature
and characteristics:
 Order: the order of the responses is significant.
 Distance: ratios scale do offer interpretable distance.
 True zero is there in the ratio scale which means in our case there is no income
(Gupta and Gupta, 2017).
Conversion of the data into information and information into knowledge
Mostly data managing is all about extracting the useful information from the collected
data and in order to do the same, data must go through the data mining process
which will help in the mining of the useful information from the data. There are
various approaches as well as tools and techniques to do the data mining and the
first step starts with the data processing (Anderson et al., 2016).
Data processing can be described as the conversion of the raw material into a
meaning full information through a process. In other words, it can be said that the
manipulation of the data is done so as to produce the results which will help in the
resolution of the issue in question (Lee and Peters, 2015).
Knowledge is defined as in-situation information. Which means the process of the
conversion of the information into knowledge by attaching the information to the
situation (Anderson et al., 2017).
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Using the hypothesis testing method of testing
1) Determine if the earning of the men in the public sector is different from
the earning of the women in the private sector
t-Test: Two-Sample Assuming
Unequal Variances
men women
Mean 32276.63 26933.2
5
Variance 1449962 975692.
5
Observations 8 8
Hypothesized Mean Difference 0
df 13
t Stat 9.70389643
3
P(T<=t) one-tail 1.27358E-
07
t Critical one-tail 1.77093339
6
1. Hypothesis
Null hypothesis: Ho: μ1 = μ2 [there is no significant difference in the earnings of
the men and women in the public sector]
Alternate hypothesis: H1: μ1 ≠ μ2 [there is a significant difference between the
earnings of the men and women in the public sector]
2. Test statistics = 9.7039
3. Level of significance
α= .05
4. Critical value = 1.770
5. Decision: if the calculated value is more than the critical value, then the null
hypothesis is rejected which means that there is a significant difference
between the earnings of the men and women in the public sector.
2) Determine if the earning of the men in the public sector is different from
the earning of the women in the private sector
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men women
Mean 28096.3
8
20541.2
5
Variance 795090.
8
988729.
9
Observations 8 8
Hypothesized Mean Difference 0
df 14
t Stat 15.9996
7
P(T<=t) one-tail 1.08E-10
t Critical one-tail 1.76131
1. Hypothesis
Null hypothesis: Ho: μ1 = μ2 [there is no significant difference in the earnings of
the men and women in the private sector]
Alternate hypothesis: H1: μ1 ≠ μ2 [there is a significant difference between the
earnings of the men and women in the private sector]
2. Test statistics = 15.99
3. Level of significance
α= .05
4. Critical value = 1.76131
5. Decision: if the calculated value is less than the critical value, then the null
hypothesis is accepted which means that there is a significant difference
between the earnings of the men and women in the private sector.
Preparation of the earning time- chart for each group and determine the
annual growth rate
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2009 2010 2011 2012 2013 2014 2015 2016
22000
24000
26000
28000
30000
25224 26113 26470 26663 27338 27705 27900 28053
women in public sector
year
earning
2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
28000
30000
32000
34000
36000
30638 31264 31380 31816 32541 32878 33685 34011
men in public sector
year
earnings
2009 2010 2011 2012 2013 2014 2015 2016
18000
19000
20000
21000
22000
19551 19532 19565
20313 20698 21017 21403
22251
women in private sector
date
earnings
2009 2010 2011 2012 2013 2014 2015 2016
25000
26000
27000
28000
29000
30000
27632
27000 27233 27705 28201 28440 28881
29679men in private sector
year
earnings
The earning time chart is been prepare for each of the group i.e. for earnings of men
and women in the public sector and earnings of men and women in the private
sector. With the help of the CAGR in excel, the annual growth rate is been
calculated.
The annual growth rate for men in the public sector: 1.31%
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The annual growth rate for men in the private sector: 1.34%
The annual growth rate for women in the public sector: 0.90%
The annual growth rate for women in the private sector: 1.63%
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LO2 ANALYSIS AND EVALUATION OF THE RAW BUSINESS DATA
WITH THE HELP OF THE STATISTICAL METHODS
Differences between qualitative and quantitative raw data analysis
Basis Qualitative data Quantitative data
Purpose The purpose is to elucidate and gain
vision and understanding of the topic
through an intensive collection of
narrative data by generating the
hypothesis to conduct the test in the
inductive manner (Storey, 2016).
The purpose is to explicate,
forecast, and/or control
phenomena with the help of the
absorbed collection of numerical
data by testing the hypotheses in
a deductive manner.
Hypotheses Cautious, developing, based on specific
study
Exact, testable, specified prior to
conducting the particular study
(Dancer et al., 2015)
Research
Setting
Measured setting not as important Controlled to the extent possible
Measurement Non-standardized, descriptive(written
word), ongoing (Moore et al., 2016)
Uniform, numerical
(measurements, numbers),
measure at the end
Data
Collection
Strategies
Data can be collected with the help of
methods like interviews or focus groups,
open-ended questionnaire, detailed filed
noted etc. (Moore et al., 2016)
Data can be collected by
administering the questionnaires
and the tests along with the focus
groups and interviews.
Data Analysis Raw data are expressed in words.
Basically continuing and involves using
the explanations to draw a conclusion.
Raw data collected is in the form
of the numbers on which the test
is been performed at the end
means it uses numbers to come
up to the conclusions (Moore et
al., 2016).
Data
Interpretation
There can be changes in the
conclusions as it is been reviewed on
the continuing basis and the validity of
the inference is the responsibility of the
reader (Moore et al., 2016).
Usually, conclusions are
formulated at the end of the study
and the generalisation and the
inference is the responsibility of
the researcher.
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Descriptive statistics
 Measures of central tendency
A measure of central tendency can be described as the summary measure that
tries to sum up the whole set of data and tries to explain it with the help of the
single value which helps in the representation of the middle of the centre value of
the data distribution. There are mainly three measures of central tendency i.e.
mean, mode and median (Quinlan et al., 2019).
o Mean: mean is also said to be the arithmetic average which is been
calculated by dividing the sum of the total observations with the number of
the total observations (Anderson, 2015).
o Median: the median is described as the middle of the distribution after
arranging the values in either ascending or descending order.
o Mode: it is described as the most frequently occurred value in the whole
distribution (Anderson, 2015).
hourly earnings (x) no. of
leisure
centre
staff
(f)
middle
value
(xi)
f * xi xi - xi (xi -
XM)^2)
f * (xi -
XM)^2)
0-10 4 5 20 -16.4 268.96 1075.84
010-020 23 15 345 -6.4 40.96 942.08
20-30 13 25 325 3.6 12.96 168.48
30-40 7 35 245 13.6 184.96 1294.72
40-50 3 45 135 23.6 556.96 1670.88
total 50 1070 1064.8 5152
 Measures of variability
A measure of variability is like summary statistics which helps in representing the
value of dispersion in the data set. Some of the variations are inevitable but the
level at which the problem occurs is at the extreme. The interquartile range is
known as the middle half of the data and in order to visualise it, think about the
median value that itself is the halfway point of the data (Lai and Williams, 2017).
calculation
1. mean = total of f*xi / total off
xm= 1070 / 50
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XM = 21.4
2 standard deviation = (variance)^1/2
variance = [f * (xi - xm)^2] / f
103.04
standard deviation = (103.04)^ 1/2
10.15
3. interquartile range
= median of upper half – median of
lower half
40 - 10
= 30
4. median
= lower limit + [(n/2 – cumulative
frequency of the preceding median
class) / frequency of the median class]
x 100
= 10 + [(25 – 4) / 23] x 100
= 19.13
 Application to the business data
There is various applicability of the measures of central tendency and the
variability on the business data (Lai and Williams, 2017). For example, if we want
to find out the average salary of the secretaries, we can calculate the average
mean, similarly median help in the finding out the value that is close to the
average commonly paid salary without considering the extreme values (Lai and
Williams, 2017).
 Comparison of the two regions
London Manchester
Median 19.13 14
Interquartile range 30 7.5
Mean 21.4 16.5
Standard deviation 10.15 7
When the measures of the central tendency are been compared for the two
locations i.e. London and Manchester, it can be said that the average hourly
earnings of London are higher than the Manchester. Also, the median for London
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is 19.13 which means that majority of the hourly earnings are close to the
average earnings which are 21.4. The standard deviation tells how much the data
deviate from the mean. The standard deviation of Manchester is less which
means the salary is closely related to mean as compared to London.
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