Statistical Analysis of Business Data: A Comprehensive Report

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statistics for management

Contents
Introduction................................................................................................................. 2
LO1 INTERPRETATION OF THE BUSINESS DATA.................................................3
Characteristics of the data.......................................................................................3
Data conversion: conversion of the data into information than knowledge..............3
Hypothesis testing...................................................................................................3
Earing time chart as well as the annual growth rate................................................5
LO2 ANALYSIS AND EVALUATION OF THE RAW BUSINESS DATA.....................7
LO3 APPLICATION OF THE STATISTICAL METHODS IN THE PLANNING..........11
LO4 COMMUNICATE THE RESULTS TOGETHER GRAPHS.................................13
A) LINE GRAPH FOR CPI, CPIH AND RPI.........................................................13
B) Scatter diagram...............................................................................................13
CONCLUSION.......................................................................................................... 14
REFERENCES..........................................................................................................15
1

Introduction
The main purpose of this unit is to help in the development of the understanding of
the usage of the procedures, tools and techniques of the business statistics which
also helps in the taking the important decisions of the business. Therefore in this
assignment in various other questions, different tools are been applied so as to learn
how various tools are been applied and how they help in the decision making
processes. In the first part, application of the normal distribution and hypothesis
testing is been developed, in the second part measures of central tendency as well
as variability is been discussed, in the third part, cost estimation is been done i.e.
calculations of the EOQ as well as the inventory policy cost is been done and in the
last part, analysis is to be done with the help of the graphs.
2

LO1 INTERPRETATION OF THE BUSINESS DATA
Characteristics of the data
In the current situation, the world is surely running on the data and there are few
characteristics of the data that helps in defining the quality of the data like the
accuracy and precision, reliability and consistency, completeness as well as
comprehensiveness, uniqueness and granularity etc. (Keller, 2015). The data used
in this part of the assignment random samples of the 1000 participants from the year
2009 to 2016 is used which are collected on the ratio scale meaning it has all the
three basic characteristics i.e. interval, the degree of order and absolute zero (Keller,
2015).
Data conversion: conversion of the data into information than knowledge
Data processing is simply referred to the conversion of the raw data into the
information that is meaningful and relevant which is further used to take the
decisions and thus the data is converted into the knowledge (Punt et al., 2016). It’s
just like a cycle where input i.e. raw data is put into a process i.e. either the computer
systems or software etc. which is then used to come up with the output i.e.
information or insights (Punt et al., 2016).
Hypothesis testing
1. To inspect the significant difference in the earing of the women and men in
the public sector
z-Test: Two Sample
for Means
men women
Mean 32276.6 26933.2
Known Variance 1449962.
2
975692.
5
Observations 8 8
Hypothesized Mean
Difference
0
z 9.7038
P(Z<=z) one-tail 0
z Critical one-tail 1.6448
P(Z<=z) two-tail 0
z Critical two-tail 1.9599
3

I. Hypothesis
Ho: The mean average salary of the men and women is the same i.e. there is
no significant difference, in the public sector.
H1: The mean average salary of men and women is not the same i.e. there is
a significant difference, in the public sector.
II. The calculated value of the Z test: 9.7038
III. Significance level @ 5%
IV. Critical value (z critical two tail value) 1.959
V. Conclusion
The null hypothesis gets rejected if the calculated value is higher than the critical
value which means alternate hypothesis gets accepted which refers towards that
there is a significant difference in the average salary of the men and women in the
public sector.
2. To check the significant difference in the earning of the women and men in
the private sector
z-Test: Two Sample for
Means
men women
Mean 28096.3 20541.2
Known Variance 795090 988729
Observations 8 8
Hypothesized Mean
Difference
0
z 15.999
P(Z<=z) one-tail 0
z Critical one-tail 1.644
P(Z<=z) two-tail 0
z Critical two-tail 1.959
I. Hypothesis
Ho: the average salary of the women and men is the same i.e. there is a
significant difference in the average salary of the men and women, in the
private sector.
H1: The average salary of men and women is not the same i.e. there is a
significant difference in the average salary of men and women, in the private
sector.
4

II. The calculated value of z-test: 15.99
III. Significance level @ 5%
IV. Critical value ( z critical two-tail value): 1.959
V. Conclusion
The null hypothesis gets rejected when the calculated value is higher than the
critical value which means that the alternate hypothesis gets accepted which
means that there is a significant difference in the average salary of the women
and men in the private sector.
Earing time chart as well as the annual growth rate
For calculating the earnings growth rate for the groups of men and women in both
the private as well as public sector, CGAR method is been put to use.
CAGR formula: [end investment value \ start value] ^ 1/ n-1
Therefore the CAGR for all the groups are as follows:
CAGR of Rate
Men in the public sector 1.31%
Women in the public sector 1.34%
Men in the private sector .9%
Women in the private sector 1.63%
Charts:
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
5

2009 2010 2011 2012 2013 2014 2015 2016
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
6

LO2 ANALYSIS AND EVALUATION OF THE RAW BUSINESS DATA
The data collection can be of two types i.e. either in the qualitative form or in the
quantitative form (Chandrasekaran and Umaparvathi, 2016). The data collected for
this question is in the quantitative form. The data collected is in the form of
quantitative data. Descriptive statistics is been divided into two parts i.e. measures of
the central tendency i.e. mean, mode or median and measures of the variability i.e.
standard deviation, kurtosis etc. (Parihar, 2018).
Measures of the central tendency
Mean
Also refers to the average of the data is used to calculate the average hourly
earnings of the London people (Siegel, 2016). Therefore it is been calculated by
dividing the total hourly earnings by the total of the number of the observant that i.e.
a total number of frequency (Siegel, 2016).
Mean = total earnings / total frequency
= 1070 / 50
= 21.4
Median
Also refers to the middle value of the data series. It is often calculated using the
formula or the ogive (Siegel, 2016).
The steps for the calculation of median are as follows:
a. Find the median class i.e. n / 2 and check where it lies in the cumulative
frequency i.e. 50 / 2 = 25, therefore the median class will be 10 – 20.
b. Formula for the median: lower limit of the median class + [(n / 2 – cumulative
frequency of the preceding median class) / frequency of the median class] *
100
c. 10 + [(25 – 4) / 23] * 100
d. Median = 19.1
7

Ogive:
Mora than ogive
0 10 20 30 40 50 60
0
10
20
30
40
50
60
more than ogive
Less than ogive
5 10 15 20 25 30 35 40 45 50 55
0
10
20
30
40
50
60
less than ogive
hourly no. of Cumulati middl f * xm Xm - m (xm - f * (xm -
8

earnings (x) leisur
e
centr
e
staff
(f)
ve
frequency
e
value
(xm)
m)^2) m)^2)
0-10 4 4 5 20 -16.4 268.96 1075.84
010-020 23 27 15 345 -6.4 40.96 942.08
20-30 13 40 25 325 3.6 12.96 168.48
30-40 7 47 35 245 13.6 184.96 1294.72
40-50 3 50 45 135 23.6 556.96 1670.88
total 50 1070 1064.8 5152
Measures of the variability
Standard deviation
It usually refers to the square root of the variance which usually helps in the
measurement of the extent of the variability of the data. It can also be said that it
helps in the measurement of the dispersion of the data.
S.D. = (variance) ^ ½
= [(f (xm – m) ^ 2 / f] ^ ½
= [5152 / 50] ^ ½
= 103.04 ^ ½
= 10.15
Interquartile range
It helps in the identification of the data outliers and the interquartile range of the data
is not being affected as the interquartile range lies in between the mid 50% of the
range of the data.
= median of the upper half – median of the lower half
= 40 – 10
= 30
Comparison between two regions: Manchester and London
London Manchester
Median 19.13 14
Interquartile range 30 7.5
Mean 21.4 16.5
Standard deviation 10.15 7
9

While comparing the measures of the central tendency and the measures of the
variability for both the locations it can be said that average hourly earnings are more
in London as compared to the Manchester and also the dispersion of the income is
also high in the London than Manchester. Also since the median is at the higher side
of London it can be said that the capped income of London is at higher sides as
compared to Manchester (Siegel, 2016).
10

LO3 APPLICATION OF THE STATISTICAL METHODS IN THE
PLANNING
Any organisation which is usually engaged in either production, selling or the trading
of the goods have to stack a huge amount of the inventory. In the question, the t-shirt
trader needs to know how much of the inventory is needed to behold and when it is
needed to place the order (Rivera, 2017). So here comes the inventory planning
which refers to the process that is adopted by the organisation for determining the
optimal quantity along with the best timing with the only aim of the alignment of the
plans with the capacity of the organisation to make sales (Horton et al., 2015).
1. EOQ
EOQ stands for the economic order quantity which is the level of the quantity to be
ordered by the company at which the company have to bear the minimum cost of the
inventory (Miah, 2016).
EOQ = [(2 x 1500 x 5) / 2] ^ ½
= [7500] ^ ½
= 87 t-shirts
2. Number of the orders to be placed
It usually refers to the complete cost of the inventory which is to be placed by the
company and is calculated using the following formula:
Total quantity / EOQ
= 1500 / 87
= 17.24 orders or 18 orders.
3. Inventory policy cost
Inventory policy is described as the cost of the inventory which includes the ordering
cost, holding cost and the total cost of the t-shirt (Richard, 2018). It is calculated with
the help of the following formula:
11