8th Edition

ISBN: 9781337672320

Author: BRASE

Publisher: Cengage

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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Textbook Question

Chapter 3.2, Problem 26P

Expand Your knowledge: Moving Averages You do not need a lot of money to invest in a mutual fund. However, if you decide to put some money into an investment, you are usually advised to leave it in for (at least) several years. Why? Because good years tend to cancel out had years, giving you a better overall return with less risk. To see what we mean, let's use a 3-year moving average on the Calvert. Social Balanced Fund (a sociallyresponsible fund).

Year	1	2	3	4	S	6	7	8	9	10	11
% Return	1.78	17.79	744	5.95	-4.74	25.85	9.03	18.92	17.49	6.80	-2.38

Source Fund Reports

(a) Use a calculator with mean and standard deviation keys to verify that the mean annual return for all 11 years is approximately 9.45%, with standard deviation 9.57%.

(b) To compute a 3-year moving average for 1992. we take the data values for year 3 and the poor 2 years and average them. To compute a 3-year moving average for year 4, we take the data values for year 4 and the poor 2 years and average them. Verify that the following 3-year moving averages are correct.

Year	3	4	5	6	7	8	9	10	11
3-year moving average	9.01	10.40	2.89	9.02	10.05	17.93	15.15	14.40	7.30

(c) Use a calculator with mean and standard deviation keys to verify that for the 3-year moving average, the mean is 10.68% with sample standard deviation 4.53%.

(d) Interpretation Compare the results of parts (a) and (c). Suppose we take the point of view that risk is measured by standard deviation. Is the risk (standard deviation) of the 3-year moving average considerably smaller? This is an example of a general phenomenon that will he studied in more detail in Chapter 6.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 3.2, Problem 25P

Chapter 3.2, Problem 27P

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Chapter 3 Solutions

Understanding Basic Statistics

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Solution Summary: The author explains how the mean return for all 11 years is approximately 9.45%, with standard deviation 9.57%. The 3-year moving averages are correct.

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