Statistics: Variance and Vanguard Total Stock Essay

1. For the following scores, find the mean, median, and the mode. Which would be the most appropriate measure for this data set?

Advisors and investors would do well to pay as much attention to the expected volatility of any portfolio or investment as they do to anticipated returns. Moreover, all things being equal, a new investment should only be added to a portfolio when it either reduces the expected risk for a targeted level of returns, or when it boosts expected portfolio returns without adding additional risk, as measured by the expected standard deviation of those returns. Lesson 2: Don’t assume bonds or international stocks offer adequate portfolio diversification. As the world’s financial markets become more closely correlated, bonds and foreign stocks may not provide adequate portfolio diversification. Instead, advisors may want to recommend that suitable investors add modest exposure to nontraditional investments such as hedge funds, private equity and real assets. Such exposure may bolster portfolio returns, while reducing overall risk, depending on how it is structured. Lesson 3: Be disciplined in adhering to asset allocation targets. The long-term benefits of portfolio diversification will only be realized if investors are disciplined in adhering to asset allocation guidelines. For this reason, it is recommended that advisors regularly revisit portfolio allocations and rebalance

2. In order to determine the average amount spent in November on Amazon.com a random sample of 144 Amazon accounts were selected. The sample mean amount spent in November was $250 with a standard deviation of $25. Assuming that the population standard deviation is unknown, what is a 95% confidence interval for the population mean amount spent on Amazon.com in November?

“The Benefits of diversification are clear. Portfolio theory has played a crucial role in explaining the relationship between risk and return where more than one investment is held. It also enables us to identify optimal and efficient portfolios.”

5. Give the standard deviation for the mean and median column. Compare these and be sure to identify which has the least variability?

Let’s assume you have taken 1000 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.

2. For the following set of scores, fill in the cells. The mean is 74.13 and the standard deviation is 9.98.

5. For the following set of scores, compute the range, the unbiased and the biased standard deviations, and the variance. Do the exercise by hand.

However, the Oxygen and pH levels are outside their healthy levels. As the level of dissolved oxygen in the water is lower then what is healthy, this can kill organisms that habituated the wetland. As well as the pH being higher than its healthy range, this can also kill organisms. The termination of these organisms can create devastating effects on the health of this environment by generating an imbalance in the ecosystem of the wetland. To ensure that the wetland remains an asset to the Canberra community, we must constantly observe the water quality in the wetland, and ensure that we are not polluting the wetland with air pollutants (NO2) and ensuring that the level of pH lowers from alkaline to be in the healthy range. (Urrbrae Wetland Learning Centre,

Scope: This question will be answered after nitrogen data collected by the University of South Florida is analyzed, along with data received from last year 's weather reports. The Tampa Bay Estuary Program is testing nitrates in a similar manner, in that they are monitoring the use of fertilizers and its effect on run off and water pollution. With contact with various estuary protection agencies and marine preservation organizations, the collaboration of other data will be incorporated in this investigation and present additional information that will be involved. This holds significant value, as it is proving or attempting to prove how rainwater can increase the levels of storm water drainage leading to increased nitrogen levels. Especially in wetlands and estuaries where there is a delicate ecosystem

The mode is the number occurring most frequently in the distribution. The results are: 19, 22, 23, 23, 23, 24, 27, 30, 32, 47. Therefore, the mode is 23.

Expected Worst Case Weighted Weighted Weighted Bond Return Return Duration Weight Return Duration Worst Case 1 12.50% 8% 8 40% 0.050 3.200 0.032 2 11.50% 7.50% 7 25% 0.029 1.750 0.019 3 10.50% 6.80% 6 0% 0.000 0.000 0.000 4 9.50% 7% 5 0% 0.000 0.000 0.000 5 8.50% 7.40% 3 35% 0.030 1.050 0.026 1.000 0.109 6.000 0.077 Face 1,000,000 Expected return 10.85% Avg worst case return 7.67% Avg duration 6

According to Rosvall & Bohlin (2014:1), risk is the price of opportunities provided by the stock market for investors. If investors would like to minimize risks of stock trading process, the portfolio investments are vital to be concentrated on (Anghelache & Anghelache, 2014:8). Besides, Goetzmann & Kumar (2008:433) also stated that portfolio investment is a great choice for investors to eliminate risk.

21. Using data from question 20, the variance and standard deviation respectively are: a. 64.80 and 8.05 b. 81 and 9 c. 60.22 and 7.76. d. none of these. 22. The standard deviation of a group of scores is 10. If 5 were subtracted from each score, the standard deviation of the new scores would be: a. 2 b. 10/25 c. 5 d. 10 23. The summaries of data, which may be

Risk has a role in individual’s lives around the world and that role can be influenced by an individual’s character and their daily life. Risk and return is affected by time when investing occurs. Time relates to the amount of time in the market which offers the highest chance of returns. The investment time frame will determine the amount of impact that investors will see, investment choices includes stocks and bonds (Kinicki, Cornett, Adair, Nofsinger, 2016).