Business Statistics For Australian Firms: Analysis And Recommendations

Case Study: Performance of Major Australian companies

Discuss about the Business Statistics for Australian Firms.

The current report aims to provide critical evaluation of the performance of the major Australian companies provided with the help of descriptive statistics. The main descriptive statistics used for evaluating the performance of the main Australian firms include mean, standard deviation and coefficient of variation. In this context, Anderson et al. (2014) stated that descriptive statistics are descriptive coefficients, which help in summarisation of data set. This could signify the overall population or a sample of the same.

The first segment of the report concentrates on providing advice to the investors regarding whether to purchase shares from a single firm or maintain a portfolio of shares. This is because such an advice is crucial in the current era due to the uncertainty of rapid growth in the existing global environment. The latter segment of the report sheds light on computing the different measures of central tendency based on the provided data. Finally, the implications of the values obtained have been discussed to depict the learning from statistics.

Table 1: Summary averages and measures for the provided group of shares

(Source: As created by author)

The above table mainly helps in illustrating the values related measure of central tendency (mean) and measures of dispersion (coefficient of variance and standard deviation). The provided data of the shares have been segregated into three groups, the first two contains 10 shares each respectively and the third group contains all the provided shares. The implications of the following statistical measures have been discussed as follows:

According to Calhoun (2015), mean is the most popular measure of central tendency, which could be used with both continuous and discrete data. The mean value of the initial 10 shares in terms of P/E ratio has been obtained as 16.60, while that for the dividend yield is 5.08. The mean values of the remaining 10 shares and the overall number of shares in case of P/E ratio are computed as 18.50 and 17.55 respectively, while those for the dividend yield are 4.80 and 4.94 respectively. This depicts the inverse relationship between P/E ratio and dividend yield of the portfolio of shares. The higher P/E ratio indicates positive future growth of a particular stock in future; while a higher dividend yield provides greater returns to the investors (Edwards, Edwards and Xie 2014). Therefore, according to the mean values, the shares 11-20 could expect to grow more in future; however, the dividend payout might be minimised.

Summary Averages and Measures of Dispersion for the Provided Group of Shares and their Implications

The standard deviation values in terms of P/E ratio for three types of shares are obtained as 9.22, 12.28 and 10.61 respectively. Similarly, the values in terms of dividend yield are obtained as 1.67, 2.01 and 1.81 respectively. In this context, Fraser (2016) remarked that standard deviation is a measure of dispersion of the data set from its mean value. The SD values depict that the second group of shares carries greater amount of risk, which is followed by the third group and the first group. Therefore, the returns associated with the second group of shares might result in significant losses for the investors due to unanticipated external risks.

In the words of Jaggia et al. (2016), the coefficient of variance helps in gauging the spread to explain the degree of variability with respect to the mean value. The coefficients of variances for the first 10 shares, last 10 shares and the overall number of shares are obtained as 0.56, 0.66 and 0.60 respectively relative to P/E ratio. In case of dividend yield, the coefficients of variances are found as 0.33, 0.42 and 0.37 respectively. Therefore, the coefficient of variance depicts that the amount of variability is nominal with respect to mean.

In the current global competitive environment, there is uncertainty prevailing in the prospect of rapid growth. The purchase of shares in a single organisation has certain merits and drawbacks, which are briefly demonstrated as follows:

• The4 purchase of one individual stock would result in minimised fees for the investors. This is because the investors are not required to incur any yearly management fee to the fund organisation for asset investment. Instead, the fee is paid at the time of purchasing and selling the share (Rhodes, 2015).Therefore, the greater the holding period of the stock, the lower is the ownership cost.
• With the help of investment on a single stock, the investors could handle taxes effectively. This is because the investors are in charge of the selling time and therefore, they control the timing of taking profits or losses.

• Holding individual share would restrict the investors in achieving diversification. The investment in a single share carries greater amount of risk in accordance with the portfolio theory and therefore, an investor is required to own between 20 and 50 stocks.
• The investors need additional time in monitoring their portfolios. This is because the investors are required to ensure that the organisations, in which they have invested, are not confronted with business problems (Selvanathan, Selvanathan and Keller 2014).

Based on the above discussion, it is evident that the investors aim to achieve maximum returns with lower amount of risk involved in the shares. This is because diversification of portfolio would help in reducing the risk of losses possible from a single stock to compensate the overall amount of the investors. From the 20 provided companies listed in the ASX, it is recommended to the investor to invest in the shares of BT Investment by taking into account the P/E ratio and dividend yield of the firm.

Although News Corp has higher P/E ratio in contrast to BT investment, the dividend yield of the former is lower compared to the former. The investors prefer to invest in shares, which have high P/E ratio along with effective dividend yield. However, the investors could diversify their portfolios by investing in AMP Limited and QBE Insurance to minimise the risk of holding a single portfolio. 

In order to arrive at the values pertaining to measures of central tendency, the provided data set has been sorted out from smallest to largest values.

Advice Regarding Purchase of Shares in a Single Organisation

Mean = (0 + 0 + 0 + 0 + 0 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 + 3 + 5)/ 15 = 1.20

Median (Middlemost value) = 1 (8^th position out of 15 values)

Mode (Maximum frequency) = 1 (repeated 6 times, which is higher than any other value)

Mean = (19 + 29 + 33 + 36 +38 + 42 + 45 + 52 + 60)/9 = 39.33

Median = 38

Mode = Not available

In order to calculate the above statistics, it is necessary to arrange the values from ascending to descending order (Tran 2016). According to the mean value obtained, it has been found that the exam has been completed within 39.33 minutes. However, the median value suggests that the students have completed the statistics exam within 38 minutes. The modal value could not be obtained in this case, as no single value has been repeated more than once in the provided set of data. This is mandatory to arrive at the modal value. However, the most effective measure of central tendency is the mean, as it takes into account both continuous and discrete data. Therefore, it could be inferred that the average time taken on the part of the selected students to complete the exam is 39.33 minutes. 

From the above discussion, it has been found that both measures of central tendency and measures of dispersion are inevitable tools to facilitate the decision-making process of the investors. From the statistical values of the stock prices obtained for the provided 20 companies, it has been evaluated that the shares 11-20 have greater possibility to grow further in future. However, the dividend payout of the investors might be minimised in the long-run.

Along with this, the investors are recommended to diversify their portfolios, instead of investing in a single stock for lowering the amount of risk to ensure steady returns. Finally, the measures of central tendency have been computed based on the provided data. The mean value has been considered as the most effective measure of central tendency and thus, the average time taken to complete the statistics exam is obtained as 39.33 minutes.

References:

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. and Cochran, J.J., 2014. Essentials of statistics for business and economics. Cengage Learning.

Calhoun, P., 2015. STAT 119 Elementary Statistics for Business.

Edwards, H., Edwards, S. and Xie, G., 2014. BizStats: A Data and Story Library for Business Statistics. In Topics from Australian Conferences on Teaching Statistics (pp. 405-410). Springer New York.

Fraser, C., 2016. Statistics for Decision Making and Competitive Advantage. In Business Statistics for Competitive Advantage with Excel 2016 (pp. 1-3). Springer International Publishing.

Jaggia, S., Kelly, A., Beg, A.B.M., Leighton, C., Olaru, D., Salzman, S. and Sriananthakumar, S., 2016. Essentials of business statistics: communicating with numbers. McGraw-Hill Education.

Rhodes, C., 2015. Business statistics. Economic policy and statistics.

Selvanathan, S., Selvanathan, S. and Keller, G., 2014. Business Statistics: Australia/New Zealand. Cengage Learning.

Tran, D.H., 2016. Business Statistics II: Syllabus: Spring 2016.