Statistical Analysis of Business Data: A Comprehensive Report

Desklib provides past papers and solved assignments for students. This report explores business statistics and data analysis.

STATISTICS FOR MANAGEMENT

Contents
Introduction................................................................................................................. 3
LO1 INTERPRETING THE BUSINESS AND ECONOMIC DATA...............................4
Lo2 Analyse and evaluate the raw business data by employing various tools and
techniques of statistics................................................................................................8
Lo3 Application of the statistical method in the business planning............................11
Lo4 Communicate the findings with the use of the appropriate charts and tables....13
Conclusion................................................................................................................ 15
References................................................................................................................16

Introduction
This unit aims at the development of the understanding of how the decisions are
being taken in the business with the help of the statistical tools and techniques. In
this particular assignment, in order to gain an insight about the importance of various
statistical tools and techniques in the decision making in the business, the practical
approach is been used where these tools and techniques are put to use. In the first
part of the report, use of the normal distribution and hypothesis testing is been done
to find out if there is a significant difference in the earning of the men and women in
both private and public sector. In the second part, measures of central tendency
were put to use whereas in the third part, statistics is been used to take the cost
related decisions and in the last part use of charts is been studied.

LO1 INTERPRETING THE BUSINESS AND ECONOMIC DATA
Characteristics of the data
In this question, the study is been done by taking the sample of the 1000 participants
in each group so as to compare the earnings of both women and men in both the
sectors i.e. private and public sectors (Siegel, 2016). The data which is collected is
on the ratio scale as the order of the data matters as the data is collected for the
year 20009 to 2016 and the distance the years are same and also there are true
zero presents which means the income is equal to the expenses or there is no
income at all. In order to perform the test, the average earning of the men and
women in both the private and public sector is been taken (Siegel, 2016).
How data is converted into information and information into knowledge
When we collect the data then the data by itself is considered useless especially at
the time of taking the important decision (Gupta and Gupta, 2017). Therefore the
companies that do not realise this tries to move towards success with the help of
getting more and more data. So some of the smart companies use the business
intelligence so as to process the data and to convert it into the information and then
tries to convert this information into knowledge (Gupta and Gupta, 2017).
Therefore by designing the infrastructure for the conversion of data into the
information and then into knowledge the companies try to better position themselves
so that it is able to respond and innovate in almost all of the phases present in the
company like the inventory management, cost management etc. (Gupta and Gupta,
2017).
Using the hypothesis method of testing
1) Check whether there is a significant difference in the earning of the men
and women in the public sector or not
(Calculations are done through excel)
T-TEST: TWO-SAMPLE ASSUMING UNEQUAL
VARIANCES
men women
Mean 32276.625 26933.2

5
Variance 1449962.26
8
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. Formulate the hypothesis
Null hypothesis: h0: u1 = u2, (there is no significant difference in the earnings
of the men and women in the public sector)
Where u1 is the mean salary of the men in the public sector and the u2 is the
mean salary of the women in the public sector.
Alternative hypothesis: h1: u1 ≠ u2, (there is a significant difference in the
earning of the men and women in the public sector).
2. Calculated value: t stats = 9.702
3. Significance level: α= .05
4. Critical value ( taken from the normal distribution): 1.771
5. Decision: the null hypothesis is rejected and the alternative hypothesis is
accepted as the calculated value is more than the critical value, which means
that there is a significant difference in the earnings of the men and women
working in the public sector.
2) Check whether there is a significant difference in the earning of the men
and women in the private sector or not
T-TEST: TWO-SAMPLE ASSUMING UNEQUAL
VARIANCES
men women
Mean 28096.375 20541.2
5
Variance 795090.8393 988729.
9
Observations 8 8
Hypothesized Mean Difference 0
df 14
t Stat 15.99967053

P(T<=t) one-tail 1.08057E-10
t Critical one-tail 1.761310136
1. Formulate the hypothesis
Null hypothesis: h0: u1 = u2, (there is no significant difference in the earnings
of the men and women in the private sector)
Where u1 is the mean salary of the men in the private sector and the u2 is
the mean salary of the women in the private sector.
Alternative hypothesis: h1: u1 ≠ u2, (there is a significant difference in the
earning of the men and women in the private sector).
2. Calculated value of t : t stats = 15.9997
3. Significance level: α= .05
4. critical value = 1.76
5. Decision: the null hypothesis gets rejected when the calculated value of the t
is more than the critical value of the t. In this case the calculated value of t =
15.997 is higher than the critical value i.e. 1.76 which mean null hypothesis is
rejected and the alternative hypothesis is accepted. Therefore it can be said
that there is a significant difference in the earnings of the men and women in
the private sector.
Prepare the earning time chart for each of the group and find the annual
growth rate
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
29679
men in private sector
year
earnings
For all the groups i.e. men and women in the public as well as a private sector
the trend line observed along with the time series chart is upward trend line
which indicates that there is a growth in the earnings of the men and women
in both the sectors. The annual growth rate is been calculated using the
CAGR formula which is as follows: [(end value/start value) ^1/n] -1.
Groups Growth rate
Men in the public sector 1.31%
Men in the private sector 1.34%
Women in the public sector .9%
Women in the private sector 1.63%

LO2 Analyse and evaluate the raw business data by employing
various tools and techniques of statistics
Qualitative data
The qualitative data is used to get the insight and understanding of the topic with the
help of the intensive collection of the expressive data by generating the hypothesis
so as to conduct the test in the inductive manner (Anderson et al., 2017). The data
collected in analysed in the continuation and also involves the usage of the
explanations so as to draw the conclusion (Anderson et al., 2017).
Quantitative data
The purpose of the quantitative data is to expand along with forecasting and
controlling the phenomena with the help of the numeric data by drawing the
hypothesis in the deductive manner (Anderson et al., 2017).
Descriptive statistics
Descriptive statistics is defined as the descriptive coefficients that help in
summarising the provided data set which can either represent the whole population
or the sample of the population (Anderson et al., 2017). Further descriptive statistics
is divided into two parts i.e. measures of central tendency which includes the mean,
mode and median and measures of variability which includes the variance, standard
deviation, kurtosis and the skewness etc. (Anderson et al., 2017).
 Measures of central tendency
In statistics, central tendency is described as the typical value or the central
value for a probability distribution. It can also be described as the centre of the
distribution. There are mainly three measure i.e. mean, mode and median
(Liu, 2017).
Mean is the average of all the observations and is calculated by dividing the
total of all the observations by a number of observations (Skordi and Fraser,
2018).
The mode is described as the most repeated value in the observation.
Median is described as the middle value that helps in separating the higher
half and the lower half of the data (Skordi and Fraser, 2018).

hourly earnings
(x)
no. of
leisure
centre
staff (f)
middle
value (xi)
f * xi xi - xm (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
CALCULATION
1. MEAN = total of f*xi / total
of f
xm= 1070 / 50
xm = 21.4
2. 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
 Measure of variability
Variability of the data refers to how much the data is been spread out or how
much the data differ from each other. In other words, variability is also
referred to as the spread or dispersion (Rayat, 2018).
Interquartile range helps in finding out the outliers in the data. The IQR is not
affected by the outliers as it is the range of the middle fifty per cent of the
data.
Variance can be described as the measure of the closeness of the data to the
average of the data (Fairhall, 2019).
Standard deviation when the square root of the variance is calculated it is
called the standard deviation and also measure the closeness of the data to
the mean of the data (Fairhall, 2019).

1. STANDARD DEVIATION =
(variance)^1/2
variance = [f * (xi - xm)^2] / f
103.04
standard deviation = (103.04)^ 1/2
10.15
2. INTERQUARTILE RANGE
= median of upper half – median of
lower half
40 - 10
= 30
0 10 20 30 40 50
0
10
20
30
40
50
60
cumulative frequency ogive
Comparison of two regions
London Manchester
Median 19.13 14
Interquartile range 30 7.5
Mean 21.4 16.5
Standard deviation 10.15 7
While comparing the data of the two locations for the hourly earnings, it can be said
that the earnings of the London are more scattered around the average earning as
compared to the Manchester which means the range of the earning in the London is
more than the Manchester. Also, the average hourly earnings in London is more as
compared to the Manchester which can be judged by the mean of the data i.e.
London average hourly earnings is 21.4 where Manchester’s average hourly
earnings are 16.5.

LO3 Application of the statistical method in the business planning
Inventory control is referred to the stock control which is a very broad concept and
inculcates many other functions within. Thus it can be said inventory control refers to
the all the aspects of managing the inventory of the business which includes the
purchasing, shipping, tracking, storage and warehousing, turnover and reordering
etc. (D’Agostino, 2017).
1. EOQ
EOQ stands for the economic order quantity which helps in finding out the
optimum quantity which should be ordered by the firm in a go, so as to have
the minimum inventory cost (D'Agostino, 2017).
D = annual demand
Ch = holding cost
Co= carrying cost or ordering cost
EOQ = [(2 x 1500 x 5) / 2] ^1/2
= [7500] ^1/2
= 87 t-shirts [exact 86.7]
2. No. of orders placed
Total average demand / EOQ
= 1500/87
= 17. 24 orders (18 orders)
3. Inventory policy cost
Inventory policy cost = total annual t-shirts purchased x cost of one t-shirt +
ordering cost per order x no. of orders + holding cost of one t-shirt x no. of t-
shirts ordered x ½
= 1566 x 10 + 5 x 18 + 2 x 1566 x ½
= 17216
4. Current service level
Service factor = safety stock / no. of lead days x demand of the t-shirts in a
day

S.F. = 150 / 28 x 4.286
S.F. = 1.25
Service level = 89% [checked with the help of the normal distribution table]
5. Reorder level at the service level of 95%
Reorder level = Average demand x lead time + safety stock
Average demand = 30 t-shirts
Lead time = 28 days
Safety stock = service factor x no. of lead days x demand of t-shirts
= .81954 (taken form normal distribution) x 4 x 30
= 98.34
Reorder level = 30 x 4 weeks + 98.34
= 218 t-shirts