Foundation Skills in Data Analysis

This document provides an analysis of sample data on regional businesses and their characteristics. It includes insights on employee count, growth strategies, and more.

FOUNDATION SKILLS IN DATA ANALYSIS
STUDENT ID:
[Pick the date]

MEMORANDUM
Dear Sir
I have analysed the sample data comprising of information about 150 local businesses which was
provided by you. In this process, statistical tools and techniques have been applied considering
the underlying requirements and the nature of data that has been presented. On the basis of the
analysis carried out, queries posted through email have been answered in the context of regional
businesses and their characteristics, The brief responses to the queries indicated in the email are
offered below.
1) The sample data highlights that on an average 30 employees seem to be employed by each
regional business forming part of the sample. However, this conclusion is not correct and
perhaps misleading when the median value is considered. This is significantly smaller at 8
employees which highlights that out of 150 businesses included in the sample, 50% do not
have employee strength exceeding 8. Under such scenario, it is illogical to conclude that
average employee per regional business is 30. Clearly, the mean value has been disrupted by
the inclusion of certain businesses which may have a high number of employees which tends
to enhance the average. Such businesses are not representative of the sample and thereby
median should be preferred over mean. Another key aspect is that with regards to employee
count in regional businesses provided as sample, the amount of dispersion is quite high. The
evidence in this regards can be provided by the high range value whereby the minimum
employee working in a regional business is only 1 while the maximum number of employees
working is 308. The graphical representation of the sample data in terms of employees also
indicates that there are small number of regional businesses which have employed quite a lot
of employees but it should not be considered as a normal trend since these few businesses
are abnormal cases or outliers. The inclusion of these businesses in the given sample has led
to distortion of vulnerable measures such as mean and standard deviation.
2) Relying on the sample data, the key aim is to draw an estimate for the proportion of total
regional businesses based in Ballarat city with a growth strategy in place. The computations
carried out in this regards hint at the proportion of regional businesses with a growth strategy
in place lying between 64.10% and 78.57%. Considering the accuracy of the estimate
considered while performing the relevant computations, there exists a 5% chance that the
average for the population of regional businesses in Ballarat city with growth strategy may
not lie in the above interval. The interval stated above is indicative of high consumer
confidence amongst regional (local) businesses as growth strategy would make sense when
the future outlook looks stable and positive.

3) A claim has been made by a industry body belonging of another city that revenues earned
may be significantly hampered if growth strategy is not pursued by atleast 76% of the local
businesses. Based on the provided sample data, testing has been done if the claim is indeed
true for regional businesses based in Ballarat city. Based on the relevant analysis, it has been
witnessed that the available evidence from the sample data does not provide any evidence to
conclude that local businesses with growth strategy is lesser than 76% for Ballarat city.
Also, analysis has been conducted to verify if the average employees working in local businesses
with growth strategy tend to exceed those local businesses which do not have a growth strategy.
The sample data has been used to derive a mean estimate lying between 25.40 and 44.07 for the
regional businesses with a growth strategy in place. For the other set of regional businesses that
do not have any growth strategy in place, the corresponding interval is expected to lie between
11.75 and 24.86. A key observation on comparison of the interval of the two sets of regional
businesses is that the mean employee strength have no overlap. This clearly supports the claim
that the difference in number of employees working in local businesses with and without growth
strategy is significant with higher mean employees noticed for the former as compared to the
latter.
4) The key objective of the test was to ascertain if your claim of managers in local businesses
located in Ballarat city being younger than their national counterparts is true or not. The
sample data does not provide support with regards to your claim as the average age for
managers working in local businesses is not less in any significant manner then 50 years
which happens to be the national average.
5) A key information which has been provided based on past trends is that on average 10
businesses open in the area. This information has been deployed for estimation in regards to
likelihood of businesses exceeding 15 annually which has been derived as 0.0487.
Considering that this is less than 5%, hence it would be abnormal to see more than 15
businesses opening up in any given year. The estimate for new businesses being 5 or less has
been computed as 0.0671 which is slightly higher than the estimate for more than 15
businesses.
6) You have specified some key requirements for accuracy based on which the next year sample
size ought to be estimated. With regards to estimation of average employee count that local
businesses employ within a error of 4 employee, the sample size of 697 is atleast required.
For the estimation of local businesses having a growth strategy with an error of 2% , the
sample size requirement is 1964 at the minimum. As you want to fulfill both the
requirements, hence the sample size of local businesses to be included in next year sample
ought to be 1,964 at the minimum.
If there are any unaddressed questions or follow-up queries regarding the analysis conducted and
related findings, please contact me.
Yours faithfully
Nick Black