Any topic (writer’s choice)

Any topic (writer’s choice)

QBM117 Business Statistics

Assignment 1

Due date:  3 August 2014
Value:   10%

Rationale
Assignment 1 is designed to assess the following learning outcomes:
  be able to explain the standard uses of Statistics in the media and in business
environments,and judge whether the statistical methodology and conclusions
drawn are appropriate.
  be able to summarise and interpret data graphically and numerically.
  be able to use a statistical package to analyse data appropriately, and then interpret
the output.
Presentation
The assignment must be neatly handwritten with any Excel output inserted where
required at the appropriate place in the assignment not in an Appendix at the back of the
assignment. Justification for requiring the assignment to be hand written is provided in
the subject outline. Use the template provided in the assignment folder in resources when
preparing this assignment.
If using EASTS, you must submit ONE file per assignment and that file must be PDF or
DOC or DOCX. Excel files are not permitted. EASTS cannot print them.

Question 1 (24 marks)

a.  A  consumer  group  asked  a  random  sample  of  20  drivers  to  keep  a  record  of  the
number of discount petrol vouchers  used by each driver over a six month period.
The data showing the number of vouchers used follows.

26   24   12   15   8   4   6   15   18   2   7   5  0   3   5   17   10   5   9   12

For these data, calculate
i.  the mean number of vouchers used.
ii.  the standard deviation number of vouchers used.
iii.  the median number of vouchers used.
iv.  the range of the number of vouchers used.

Use the statistics functions on your calculator for parts i. and ii. above. Do not use
the formulae provided in the text.
(4 marks)

b.  The opening daily share price for the Commonwealth Bank for the period 3/3/14
to  2/7/14  inclusive  averaged  $78.84 with  a  standard deviation  of  $2.45.  The
opening daily share price  in  Origin  Energy for  the  same  period averaged  $14.67
with a standard deviation of $0.35.

i.  Calculate  the  variability  of the daily share price for  each  company by
calculating the coefficient of variation.
ii.  Based  on  the  coefficient  of  variation calculated  in  part  i.,  which  is  the
riskier company to invest in? Explain.
iii.   Why  is  the  coefficient of  variation  a  better  measure  of  risk  than  the
standard deviation in this case?
(6 marks)

c.  The boxplot which follows shows the daily closing prices for Commonwealth
Bank shares for the perod 10/4/14 to 2/7/14 inclusive.

76 77 78 79 80 81 82 83
price per share  ($)
Boxplot showing  closing  prices for Commonwealth
Bank shares 10/4/14 to 2/7/14
BoxPlot

Use  the boxplot above to answer the following questions.

i.  Would the mean closing price over this period be higher or lower than the
median? Justify your answer. Calculations are not necessary.
ii.  Estimate the lowest closing price to the nearest 50 cents. Is this an outlier?
Justify your answer.
iii.  Complete  this  sentence.  Fifty  percent  of  the  closing  prices  are  between
_________ and _________. Express each amount to the nearest 50 cents.
(7 marks)

d.  The  weekly  income  for a  sample  of seventy  randomly  selected petrol  stations in
NSW was recorded in a given week. The data were summarised and presented in
the table which follows.

Weekly income ($’000s)  Frequency
>   20 up to and including   40  6
>   40 up to and including   60  9
>   60 up to and including   80  25
>   80 up to and including 100  20
> 100 up to and including 120  8
> 120 up to and including 140  2

Use the statistics functions on your calculator to determine the approximate
mean and standard deviation weekly income for petrol stations in NSW.

Do not use the formulae provided in the text.
(3 marks)

e.  Identify  whether  the  following  proposed study  is  an  example  of  descriptive
statistics or inferential statistics and justify your choice.

Estimating the true proportion of households in Canberra that have at least three
dependents, from a random sample of 100 Canberra households.
(2 marks)

f.  Data was collected on the incomes of all employees in a large company. What is
the most likely shape of the distribution of these incomes? Justify your choice.
(2 marks)

Question 2 (62 marks)

Download  the  data  set ‘auction data.xls’ from  the Assignment  folder  in  the resources
section of Interact. The data provided in auction data.xls show the Sydney auction results
for  the  week  ending 22 June  2014.  The  variables  in  this  data  set  are: Beds,  Type,  Price
and Result representing the number of bedrooms, the type of property (house or unit), the
selling price (if sold) and the result of the auction respectively, as well as the auction date
and the name of the selling agent.

a.  For each of the variables in the list below, identify the type of data recorded. State
whether it is quantitative or qualitative and include the level of the data (nominal,
ordinal, interval or ratio).

i.  Beds
ii.  Type
iii.  Price
(6 marks)

b.  Most real data  sets  you  encounter  will contain errors. This  one  is  no  exception.
Read the document ‘working with real data sets.pdf’ which explains how to
identify  errors  in  a  data  set  and  how  to  deal  with  them before  going  any
further.

List any four different types of errors you have found in this data set and explain
why for  each  one  why you  have  decided it  was  an error or  possible  error.  For
example do not list four entries which all had the price missing.

You  may  want  to  leave completing this question till later. As you work with the
data  set  you  will  encounter some  of  these errors  so  just  make  a  note  of  them  as
you find them.

Since we cannot contact the real estate agents to follow up on these errors, for the
purpose of this assignment we will work with the data set as best we can.
(4 marks)

c.  Sharon and Mark are property owners in  the  Sydney  region who are planning  to
sell their two bedroom unit over  the  next  few  months. They are considering
putting it up for auction so are interested in using these data to gain an insight into
the current Sydney auction market.

Using  the complete data set, generate a three way pivot table report of ‘beds’ by
‘type’ by ‘result’. Use ‘type’  and ‘beds’ as row labels.

Include the table as part of the submitted assignment.

Use the data in the pivot table to answer the following vendors’ questions about
the properties listed for auction in Sydney for the week ending 22 June 2014.

i.  How  many  properties  were  originally listed  for  auction for  the  week  in
question? How many of these were units?

ii  How many houses were withdrawn from sale? How many units were
withdrawn from sale?

iii  How many 2 bedroom units were passed in? Express this as a percentage
of all the units listed for  auction that  week excluding all units that  were
withdrawn from sale.

iv.   How many 2 bedroom units were sold at auction that week? How many 2
bedroom houses?

v.  Of all  the  properties listed  for  auction,  how  many 3  bedroom units,
including those that were sold prior to and those that were sold after,were
sold that  week? Then,  express this  as a percentage  of all the 3 bedroom

units listed for  auction that week excluding those  that  were  withdrawn
from sale.
(13 marks)

d.  Separate the data into two data sets, one consisting of the units data only and one
containing the houses data only.

i.  Use  Excel  to  generate separate tables of  descriptive  statistics for  houses
and  units for  the  variable Price’ and  include them in  your assignment
submission. Round  both  means  to  the  nearest  thousand  dollars  and  both
standard deviations to the nearest ten dollars.

ii.  What was the price of the cheapest property sold that week? Look further
afield  to include  information  about what  type  of  property  it  was,  how
many  bedrooms  it  had,  whether  it  sold  at  auction  or  before  or  after,  and
which real estate agent sold it.

iii.  The sample variance may have been expressed in an unusual way in one or
both  of  these tables generated  in  part (i.). Explain  this  unusual  notation
and the numerical value it represents (in one or both tables).
(8 marks)

e.  Using  the data  set for units only,  use  Excel  to  prepare  a  frequency  distribution
and histogram of the variable ‘Price’ for the unit data. Use $500 000 as the upper
limit of the first class and a class width of  $500 000.
(5 marks)

f.  After  preparing  this  histogram, discuss  whether the  choice  of  classes  suggested
above is appropriate. Refer to important aspects such as the number of classes, the
width of the classes and whether all data are included in the classes chosen.
(3 marks)

g.  Generate a boxplot for the variable ‘Price’for  the units data  only. Include  the
5-number  summary  generated  by  Excel  and  the  boxplot  with  your
assignment submission.
(4 marks)

h.  Answer the following questions regarding the data for the units only and indicate
the particular output in (d), (e) and (g) which provided the answer.

i.  How many units had a sale price listed?

ii.  How many outliers are there in the distribution of the selling prices of
units ? What is the value of the largest outlier?

iii.  25% of units sold for $x or less. What is x?

iv.   Comment on the shape of the distribution of the ‘Price’ variable for units
only (skewed,  symmetric,  direction  of  skewness  if  relevant,  unimodal,
bimodal,etc.). Provide at least three items of supporting evidence from the
output generated in parts (d), (e) and (g).
(10 marks)

i.  If a media outlet were to quote the average selling price (of units listed for auction
that week), would it be more appropriate to quote the mean or the median price?
Why?
(2 marks)

j.   Sharon  and  Mark would  like  to  know  the  selling success  rate  of  the all  the
properties that  were  listed. For all  the properties that  were  listed  for  auction,
generate  a two way pivot table of ‘Type’ by ‘Result’.(Hint: include ‘Result’ in
both  the  column  and  in  the  body  of  the  table.) From  this  pivot  table,  generate a
single horizontal 100% component bar chart with the variable ‘type’ plotted along
the vertical axis  and  the different types of ‘result’ making  up the  components of
each bar. Include both the pivot table and the bar chart with your assignment
submission.

Would  it  be  correct  for Sharon  and  Mark to  conclude  from  this  chart  that more
units than houses were sold prior to the auction? Explain.
(7 marks)

NB Don’t forget to go back and complete Q2 part b.