Question

Returns on stock X are listed below:

Period	1	2	3	4	5	6	7
Stock X	8%	0%	3%	-2%	5%	12%	7%

What is the (population) standard deviation of the data?

Please specify your answer in decimal terms and round your answer to the nearest thousandth (e.g., enter 12.3 percent as 0.123).

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

Answer 1

Data:

Period	1	2	3	4	5	6	7
Stock X	8%	0%	3%	-2%	5%	12%	7%
Stock X (in decimal)	0.08	0.00	0.03	-0.02	0.05	0.12	0.07

We get the stock X (in decimal) by dividing the stock X values by 100%

To get population standard deviation we can use Excel

using Excel it is very easy

1) just input the period and Stock x(in decimal ) data in two different column of excel

2) select a blank cell in excel file where you want the answer

3) Type in the cell '=STDEV.P(select the Stock X(in decimal) column)'

4) you will get the answer 0.04463

After rounding the answer we get 0.045

This can also be done with out excel also by calculating in hand

Let Xi be the data of the variable Stock X (in decimal) for i th period

Formula of standard deviation (population) :

mean = average of Stock X(in decimal) = (0.08+0+0.03-0.02+0.05+0.12+0.07)/7 = 0.047143

n= number of data in variable Stock X (in decimal)

so using the formula we get equation

after computing we get 0.04463

Rounding the answer to nearest thousandth we get 0.045

Answer: Population Standard Deviation =0.045