Question

\(\underline{\text { Question } 3 .}\)

The following returns were realized on an investment over a 5 -year period.

$$ \begin{array}{lccccl} \text { Year } & 1 & 2 & 3 & 4 & 5 \\ \text { Rate of Return } & .10 & .22 & .06 & -.05 & .20 \end{array} $$

1. Compute the mean and median of the returns.

2. Compute the geometric mean.

3. Which one of the three statistics computed in parts (a) and (b) best describes the return over the 5 -year period? Explain.

Answer 1

We are given the rates of returns on an investment for 5 year period as shown below.

Year	Rate of return
1	0.10
2	0.22
3	0.06
4	–0.05
5	0.20

a) We need to compute the mean median and mode fort eh above data.

Mean: Using EXCEL software to obtain the mean the instruction set is as follows:

1) Type or import data into one or more columns (A1 to A5)

2) Type into an empty cell =AVERAGE (A1:A5).

3) The active cell would store the mean as 0.106.

Therefore, the average rate of return for the 5 year period is 0.106.

Median: Using EXCEL software to obtain the median the instruction set is as follows:

1) Type or import data into one or more columns (A1 to A5)

2) Type into an empty cell =MEDIAN (A1:A5).

3) The active cell would store the median as 0.10.

Therefore, the median rate of return for the 5 year period is 0.10.

b) We need to compute the geometric mean for the above data.

Let denote the rate of return in period i (i=1, 2, 3, 4, 5). The geometric mean can be calculated as follows:

First calculate the as shown in the below table.

Year	Rate of return
1	0.10	1.10
2	0.22	1.22
3	0.06	1.06
4	–0.05	0.95
5	0.20	1.20

Use EXCEL software to obtain the geometric mean by using the following instruction set:

1) Type or import the values of in to a column.

1) Type or import data into one or more columns (A1 to A5)

2) Type into an empty cell =GEOMEAN (A1:A5).

3) The active cell would store the mean as 1.102.

Therefore, the geometric mean for the data is 1.102.

c) We need to verify the suitable measure for the data among all measures computed in parts (a), and (b).

Here, we are given rates of five years data; as we know that the geometric mean is the suitable measure when the data is given in the rates or percentages, Geometric mean is the suitable measure for the rates data of five year period.