Foundation Skills in Data Analysis

This document discusses the foundation skills in data analysis and the use of statistical techniques. It analyzes a sample data set of 150 regional businesses and provides insights on various aspects such as the average number of employees, proportion of businesses with growth strategy, comparison of average age of managers, and estimation of probabilities. The document also highlights the accuracy requirements for prediction and the minimum sample size needed for different scenarios.

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

MEMORANDUM
Dear Sir
Taking into consideration the sample data of 150 regional businesses which you had provided, a
data analysis has been performed using the suitable statistical techniques. The analysis using the
data has been performed considering the underlying question which ought to be answered. The
given memo aims to highlight the responses with regards to the various queries raised by you
through the email sent earlier. The responses to the various questions posed are illustrated below.
1) Based on the sample data, the average number of employees that a regional business included
in the sample employs is 30. However, the corresponding median value is only 8 which
clearly highlights that the mean value is inaccurate. The reason for this inaccuracy is that
there are some regional businesses which are part of sample and have a high number of
people employed. The mean value has been skewed by these extreme values and thereby
presents a distorted picture. The better indicator of the central value with regards to the
employees with each regional business would be median which has a value of 8. This would
indicate that 75 of the regional businesses that are part of the sample have employee strength
not exceeding 8. The high variation in the number of employees is reflected from the
difference in the minimum and maximum values. The maximum value of employees
working at a regional business is 308 while the minimum value is1. Based on the graphical
illustration of the distribution of employees, it is apparent that the shape is quite skewed
owing to presence of firms having a large number of employees but these are quite limited in
number. However, these firms still have a managed to produce a distortion in the sample data
and various summary measures.
2) The proportion of regional businesses with growth strategy in Ballarat city needs to be
estimated using the sample data provided. Based on the relevant computations, it would be
fair to estimate that this proportion of regional businesses with growth strategy located in
Ballarat city would lie in the interval defined by outer limits of 64.10% and 78.57%. It is key
to note that a 5% chance does exist whereby the requisite proportion would not fall in the
above interval. Considering that majority of the regional businesses have a growth strategy in
place, this is representative of the superior business confidence that the businesses have with
regards to the future potential and opportunities.
3) The Clunes Chamber of Commerce has claimed that it is essential that growth strategy
should be witnessed for 76% of the regional businesses in order to avoid revenue loss. There
is concern in the Ballarat Council in this regards and hence requisite test has been conducted

to test the performance of regional businesses under your council to determine their
performance in context of growth strategy. The test highlights that the proportion of
businesses situated in Ballarat city with a growth strategy is not lesser than 76%. Therefore,
this does not seem a pressing issue.
The estimation of mean employees that a regional business employs has been made considering
the underlying strategy pursued. This has been done to test if number of employees hired by the
regional business is higher on average for businesses with growth strategy when compared to
those without growth strategy. It can be outlined that regional businesses pursuing growth
strategy on average tend to employee ranging between 25.40 and 44.07. The corresponding
interval for those regional businesses where growth strategy is absent ranges between 11.75 and
24.86. Since, the two intervals do not have any overlapping area, hence it would be correct to
conclude that there is significant difference between the number of employees hired by regional
businesses with growth strategy as against those which do not have one. Also, on average higher
employee strength maybe witnessed for regional businesses with growth strategy.
4) The aim is to compare the average age of managers for business based in Ballarat city with
the national trends witnessed in this regards. Considering the sample data, your claim
regarding younger managers for local businesses does not seem to be true. This is because
the average age of the managers employed in local businesses does not seem to be lesser than
50. Hence, the trends with regards to managerial age do not tend to differ for the city and the
country as a whole.
5) The information based on empirical trends has been provided which highlights that in an year
10 new business open on average. This has been used to estimate the corresponding
probability for the number of new businesses in an year to be higher than 15. The
corresponding value has come out as 0.0487. Similarly, the probability associated with 5 or
less new businesses being set up in the city has also been computed which has come out as
0.0671. It is clear from the respective probabilities value that the chances of more than 15
businesses opening in a year in Ballarat city seem abnormally low.
6) Considering the accuracy requirement in prediction, the minimum sample size had to be
determined for different scenarios. For estimation of mean employees which are employed
by local businesses with a margin of error of only 4employees, the required sample size
should be atleast 697. However, if proportion of local businesses with a growth strategy
ought to be estimated with a margin of error of 2%, then the required sample size should be
atleast 1964. As highlighted in your email, you want to fulfill both the conditions in terms of
accuracy of estimates and hence the minimum sample size for the next year would be 1.964.
For any further questions or clarifications required in regards to responses above, feel free to
email me,
Yours Sincerely
Nick Black