0:05

Hello and welcome to the third module.

Â Today we are going to travel together to the Swiss village called Sunnydorf.

Â Sunnydorf is a small village by the Swiss lake, inhabited by 16 men and women.

Â Well obviously these 16 men and women are different in their height.

Â Some are bigger, some are smaller.

Â Another difference of the inhabitants of this village is the amount of money that

Â they have in their bank account, some of them are very rich,

Â some of them have just very little money.

Â So today we're going to take data about the height and wealth of the inhabitants

Â of Sunnydorf and learn a little bit more about random variables.

Â If we go to our table here, on the right of our document we have the information

Â about the height and the wealth of the inhabitants in Sunnydorf.

Â We have an inhabitant ID for each of those, and

Â additionally we have some data here about the wealth in US dollars of these

Â inhabitants after winning the lottery.

Â This is something that we will use for a later question.

Â So, as we see we have different heights for

Â different inhabitants, and different amounts of the money in the bank account.

Â Some have very few, some have very much.

Â Now let's use the information to answer some questions.

Â 1:27

The first question asks us to compute the arithmetic mean of the height and

Â the the wealth of their population.

Â Well in Excel,

Â we can calculate the arithmetic mean by using the formula AVERAGE as we see here.

Â If we want to calculate the average in height we would just take the command

Â AVERAGE here, and select the corresponding column in the data that I just showed.

Â 1:52

If we would like to do this with the wealth, we would do exactly the same

Â command, just AVERAGE, but instead of using column K4 to K23 in Excel,

Â we would move to the column L4 to L23, where we have the data about the wealth.

Â These would be the reasons.

Â 2:10

Now we have an extra person.

Â Compute the Standard Deviation and Variance in height and wealth for

Â the population in Sunnydorf.

Â Well to calculate the Standard Deviation and the Variance, we can use these

Â formulas, STDEV.P or .S for the Standard Deviation.

Â The only difference in these two formulas is that we would use the one with .P if

Â in our data we would have the whole population, which is the case now,

Â we have the whole population of the village.

Â If we would only have one sample meaning some inhabitant of the village,

Â we would use the same formula but with .S for sample.

Â Similarly we would calculate the variance for

Â the population with the .P and the variance for the sample with .S.

Â So, if we apply the formula here, STDEV.P for the same data.

Â Meaning for the height in the inhabitant,

Â we would have a standard deviation of 13.003 for

Â the height and a standard deviation

Â of 12078299 for the wealth.

Â So as we see the standard deviation in the height is much,

Â much smaller than the standard deviation in the wealth.

Â Similarly, we would get the results for

Â the variance, which as well, differ very much in the absolute value.

Â The new question is an interpretation question into which we will use

Â the standard deviation, the variance that we just calculated.

Â And the question is if a new inhabitant was about to move to Sunnydorf, and

Â you would have to make a guess about her height and

Â wealth, for which of both variables would you

Â think that your error (measured in the units of each variable) would be smaller?

Â Well here we know that the intuition about the standard deviation is that,

Â if the standard deviation is small, then the values are much,

Â much more concentrated around the mean.

Â 4:12

This is what we see in the case of the height.

Â And this is also a logical thing.

Â The height of a man or a woman is constrained between much,

Â much smaller values than the wealth of a man, of a woman.

Â So, if we would do a prediction about the height and the wealth of a new inhabitant,

Â we would probably do a much, much smaller error in predicting the height.

Â Although we would have no idea about the height of this person, than

Â in predicting the wealth, due to these differences in the standard deviation.

Â 4:43

Now, we can play a little bit with our data to answer another question.

Â Assume that all the inhabitants of Sunnydorf would buy a lottery ticket

Â together, and decide to split the prize in equal shares if they win.

Â Well, congratulations to them because they won the prize.

Â Now, each inhabitant receives a share of $10,000

Â additionally to the wealth that they had at the beginning of this exercise.

Â The question is, how would this affect the Average, Variance and

Â Standard Deviation previously calculated?

Â Well, you learned some rules about transformations with

Â Carl in the theory slots.

Â We now just need to apply these rules, so we know that applying these calculation

Â rules, adding a constant to an expected value which is what we are doing here,

Â we're just adding 10,000 to the existing wealth, in this case,

Â to the mean, increases the value by this constant.

Â So if we would calculate the new average,

Â as we do here, we could compare this value with the previous value that we

Â calculated, average value and see that this value is 10,000 units,

Â in this case US dollars, higher than the one before.

Â Similarly, if we want to apply the calculation rules,

Â we know that the variance and the standard deviation

Â would not be affected by just adding a constant to the values.

Â Such to the standard deviation, and

Â obviously also the variance would remain constant.

Â 6:10

Thank you very much for having attended the third exercise.

Â I hope that now you know a little bit more about random variables and

Â how to cope with the different rules,

Â that you enjoyed, and hopefully see you in the fourth module.

Â Have fun.

Â