Statistics for Management Assignment: Earnings and Analysis

This statistics assignment presents a comprehensive analysis of earnings in both public and private sectors, employing hypothesis testing to compare male and female incomes. It utilizes Excel to create time charts illustrating earnings trends from 2009 to 2016 and calculates annual growth rates for each group. The assignment further delves into the leisure staff's hourly earnings in London using Ogive charts to estimate the median and quartiles, along with calculating the mean and standard deviation. Moreover, it covers inventory management by calculating the Economic Order Quantity (EOQ), reorder levels, and service levels. Lastly, the assignment analyzes economic indicators, including the Retail Price Index (RPI), Consumer Price Index (CPI), and CPIH, using line graphs to demonstrate changes over time and includes an ogive chart of cumulative percentage of leisure staff employees and its impact over their earning on hourly basis.

STATISTIC FOR
MANAGEMENT

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
ACTIVITY 1 ...................................................................................................................................1
1.a Determination of earning of men and women in public sector with hypothesis testing.....1
1.b Determining the earning of men and women in private sector through use of hypothesis
testing..........................................................................................................................................2
1.c using excel sheet for drawing the earnings of time chart of each group in Table A for the
period 2009-2016........................................................................................................................3
1.d Identifying annual growth rate of earnings of each group ...................................................5
ACTIVITY 2 ...................................................................................................................................5
2.A.a Using Ogive for estimating median hourly earnings along with quartile.........................5
2.A.b Extracting mean and standard deviation on basis of hourly earnings of leisure staff.......8
ACTIVITY 3 ...................................................................................................................................9
a) Calculating economic order quantity .....................................................................................9
b) How often order and cost .....................................................................................................10
C) calculating inventory policy cost .......................................................................................10
d) identifying current service level ..........................................................................................10
e) finding re- order level ..........................................................................................................10
ACTIVITY 4 .................................................................................................................................11
4 A)Showing change in CPI, CPIH and RPI using the data of office of National Statistics
produce line...............................................................................................................................11
4. B) Showing ogive chart of cumulative % of leisure staff employees and its impact over
their earning on hourly basis.....................................................................................................13
Interpretation..................................................................................................................................13
CONCLUSION .............................................................................................................................13
REFERENCES..............................................................................................................................15

INTRODUCTION
Statistics is study of observation in which the data is organised, interpreted, colle4cted,
presented and analysed. The statistics is used for analysing the data for interpreting their result
which assist in making right decision for the management. This analysis is used for allocating
and summarising the data in mathematical form. This assignment will provide understanding
about the earnings of men and women employed in public and private sector. Also, It will
include information about the number of leisure staff in the help of ogive in London area.
ACTIVITY 1
1.a Determination of earning of men and women in public sector with hypothesis testing
Hypothesis testing in statistics is used in which analyst test the assumptions regarding
the population parameter.
The two hypothesis consist of Null and alternative hypothesis.
Null hypothesis(H0) will provide understanding that there is no difference in the earning
of male and female working in public sector (Guo, Hu and Lei, 2017). Whereas alternative
hypothesis(H1) will provide understanding that there are significant difference in the earnings of
male and females.
Interpretation : From the above table it can be interpreted that T test for identifying the
difference between the earnings of males and female shows that there are no significant
difference in their earnings in public sector. Also, the table shows that the P value is higher than
1

0.05 which shows that the earning of the males and females are different. From the table it can be
interpreted that the average earning of males and female are 32276 and 26929 have also the
degree of freedom as shown above is 14.
1.b Determining the earning of men and women in private sector through use of hypothesis
testing
In this also, the null hypothesis will represent that there is no significant difference in the
earning of men and women in private sector. Whereas , alternative hypothesis will show that
there are significant differences in the earning of men and women in private sector.
Interpretation : From the above calculation it can be interpreted that the the p value
shown above provide understanding that it is higher than 0.05 which means there is absence of
significant differences in earnings of male and females in private sector. Also, the average
earning of the men and women shown above has provided with 28062 and 20541. So, it can be
said that alternative hypothesis is not accepted as there is no difference in their earnings.
1.c using excel sheet for drawing the earnings of time chart of each group in Table A for the
period 2009-2016
2

Interpretation : from the above table and graph it can be interpreted about the gross
annual earning of male in both public and private sector for the period 2009 to 2016. On the
basis of male earning earning in private sector it is identified that there is increase in their
earning but is less proportion. but In 2016 there is increment in their earning by 2.76%. It is
identified that earnings or private sector is raising rapidly than the public sector. It shows that
private sector have more potential which is shown from the variation in the earnings of male in
public and private sector.
3

Interpretation : From the above it is interpreted about the gross annual earnings of
females which shows that there is increase in the female earning more in public sector as
compared to private sector. It shows that female earning in the year 2010 was 26113 and in year
2016 it reached to 28053. The females employed in publi8c sector are more as compared to
private sector.
1.d Identifying annual growth rate of earnings of each group
4

Growth rate of females in private sector : From the above table it can be interpre4ted
that the females in private sector are more involved as they are giving more priority to this sector
rather than public sector. It shows that in 2016, It increased by 4%.
Growth rate of females in Public sector : The table shows the changes in earning of the
females in public sector. It shows that the earning of female in 2013 were the highest which was
the changes of around 2.6% but in 2016 the changes declines to 0.5%.
Growth rate of male in private sector : It can be interpreted that the gross annul earning
of the male in private sector were highest in he year 2016 which shows the change of 2.8%. also,
it shows that there was least increase in year 2014 by 0.85%.
Growth rate of male in public sector : It shows that the annual earning of males in
publi8c were highest increased in year 2015 and it was least increase in year 2011.
ACTIVITY 2
2.A.a Using Ogive for estimating median hourly earnings along with quartile
Ogive is used as cumulative frequency polygon. It assist in identifying the estimate
number of observations which are less or equal to the particular value. This are shown from left
to right. Ogive is used for estimating the median which is the middle value of the observations.
In this ogive chart, cumulative frequencies are considered as cumulative percent are summed and
elaborated that frequencies are very important as per implication plotted in statistics form. It
5

helps leader for obtaining quick estimate about its number of observation which bis less than or
might be equal.
Median
The value of median directly classifies about higher or lower half of sample data which is
mostly to fall below or above. In simpler term, this is replicated as middle value which is present
in numerical list and stated as measure of central tendency to be extracted.
Median : L+Cf-n/f*I
=10+(20-10)/ 23 * (25 - 4)
=19.13
6

Interpretation : From the above chart and graph it can be interpreted about leisure
employees hourly earnings. It identified that there is increase in staff during 10 to 20 but then it
is showing downward slope which shows there is decrease in number of employees. On the last
slot the cumulative frequency is 50 which shows it is good.
Quartile : It divides the observation into quarters which consist of Q1, Q2 and Q3 which
shows the variation in different observation (Koutras, Koutras and Yalcin, 2016.). The first
quartile is about 25th percentile, second at 50th percentile which is same as median and third
quartile is 75th percentile.
Quartile Result
7

1 13.7
2 19.13
3 28.08
Interpretation : The above table is articulating about quartile which is clearly depicting
about all there quartiles as 1st at 25th percentile is 4, 2nd at 50th percentile as 7 and 3rd at 75th
percentile of 13. it could be elaborated that 25% of data is smaller than 4 and 75% is higher.
With reference to second quartile, it directly reflects about median as half data is smaller and half
is higher than compared to value. Lastly, third quartile is 13 which is 75th percentile (Quartile,
2019).
2.A.b Extracting mean and standard deviation on basis of hourly earnings of leisure staff
Mean
Mean in the statistical context, can be defined as the middle valuer of the set series. It
helps in determining the central tendency of the series. The mean of a series is calculated either
by determining its average or by determining the frequency measure.
Mean: Total of FX/ Total of F
= 1070/ 50
= 21.4
From the above calculation, it can be interpret that the mean of the series has been
calculated as 21.4 which represents the frequency 20-30. this measure has been arrived as the
leisure of the employees is maximum in this frequency.
Standard deviation
8

Standard deviation is a statistical measure that helps in determining the variability of the
frequency. It is calculated through measurement of squared deviation of each frequency with the
help of its mean.
Interpretation
From the above calculation, it can be interpret that the standard deviation of the present
series comes to 10.15. This standard deviation is showing that the highest earning of the staff.
ACTIVITY 3
a) Calculating economic order quantity
Economic order quantity is referred as ideal order quantity a organization must purchase
for purpose of inventory to give set of cost of production along with certain rate of demand and
other variables as well. Generally, it is done through minimizing inventory holding costs along
with other related costs as well. Its main objective is to determine optimal number of product
units in such order when organization could minimize its costs on basis of buying and
undertaking delivery and to store units.
9

b) How often order and cost
C) calculating inventory policy cost
d) identifying current service level
The current service level of customer is equal to 95% and Z score as 1.65
e) finding re- order level
Reorder point is referred as level of inventory which directly triggers action for
replenishing particular inventory stock. This is replicated as minimum amount of item as firm
holds stock such that if stock falls to this specific amount then item should be recorded. It is
referred as very interesting concept for purpose of optimisation of inventory and automation of
inventory as well.
10