Q1: Case Study: Performance of major Australian companies (20%)

Measures such as the price/earnings (P/E) ratio, dividend yield (div yld) and market cap are some of the indicators used to measure the performance of a share. The P/E ratio is a market value indicator that shows the number of times the market price of a share exceeds the earnings per share. It is an indicator of the market’s anticipation of future earnings and the quality of past earnings. The P/E ratio is calculated by dividing the share price by earnings
per share. Dividend yield measures the simple rate of return from dividend payments.

The attached excel file presents these indicators for a sample of 20 shares listed in the Australian Stock Exchange as at 1 November.

Your task is to analyse the data and prepare a report. Your report should contain:

(i) Summary averages (ie, mean) and measures of dispersions (ie, coefficient of variance and standard deviation) for the following groups: shares: 1-10, shares 10-20 and all shares 1- 20. What do these statistics tell you? Discuss. (12 marks)
(ii) Knowing that the world economy has considerably slow down following the global financial crises (GFC) and Euro zone crises, and the prospect of rapid growth remains uncertain in the current global environment, what is your advice to an investor who wants to buy some shares in one single company. Which share you will suggest and why? Discuss. (8 marks)

Note: Your report should have an executive summary (about 5-8 lines), introduction (8-12 sentences), analysis (ie, the main body of the report), summary (5-10 sentences) and references.

Q2: Two short questions (10%):

(2a) The following table shows the number of days workers were absent from an office in Darwin the last.

0 1 1 3 0 0 2 5 0 1 1 2 0 1 1

(i) Calculate the mean, the median and the mode (4 marks).

(2b) The mid semester examination for a statistics course had a time limit of one hour and ten minutes; however, like most statistics unit it was a very easy exam. To assess how easy the exam was, the lecturer recorded the time taken by a sample of nine students who handed in their papers in less than one hour.

33 29 45 60 42 19 52 38 36

(i) Calculate the mean, the median and the mode (4 marks).

(ii) Describe what have you learnt from the statistics calculated in part (2bi) (2 marks).