Calculating Variance/ Standard Deviation from a probability model

[Officialmax90]

Hi guys, anyone know how to work out expected value using the Texas BA II Plus, so using the STAT/DATA function to work out the below Expected value, then standard deviation of EV.
Probability EPS
10% £ 1.80
20% £1.60
40% £1.20
30% £1.00
Expected Value= 1.28. but how would you use the Texas BA to calculate EV and Stadard deviation/Variance????

 

[Harrogath]

It’s easy, look.
You will calculate EV as (0.1 x 1.8) + (0.2 x 1.6) + (0.4 x 1.2) + (0.3 x 1.0) and variance of the EPS right?
With the calculator press the following:
2nd DATA
2nd CLR WORK (to prevent pass data that can interfer with this new calculation, do it always)
2nd DATA (again, we will enter values now)
X01 = 0.1 ENTER
Y01 = 1.8 ENTER (note we have 2 series of data we can fill, one is the Prob serie (X) and the other is EPS serie (Y))
X02 = 0.2 ENTER
Y02 = 1.6 ENTER
X03 = 0.4 ENTER
Y03 = 1.2 ENTER
X04 = 0.3 ENTER
Y04 = 1.0 ENTER
2nd STAT (now you have many calculations made automatically, press down button to look for them)
For variance or SD of EPS look for “Var y” and “SD y” respectively. (Wrong, see below)
For Expeceted value of EPS look for the “EXY” symbol, there you will have that 1.28 value.
Hope this helps.
GL

 

[tickersu]

Harrogath wrote:
2nd STAT (now you have many calculations made automatically, press down button to look for them)
For variance or SD of EPS look for “Var y” and “SD y” respectively.
Hope this helps.
GL

This doesn’t work, because it excludes the probability weightings on each scenario. You need to manually incorporate them. Just run the calculation the “long way”.
[Prob(1)* ((EPS1 - MEANeps)^2)]
Do this for each case, summing, and you have the variance. Take the square root of the variance to arrive at the standard deviation. I got 0.0736 for the variance.

 

[Iampossible]

Was quite excited for a moment there.
But clearly the calculator method does’t give the correct answers for the variance or the standard deviation.
The correct variance is 0.0736 while the standard deviation is 0.2713.
Your TI will give you the population standard deviation as 0.1118 and the sample standard deviation as 0.1291, neither is correct.
It gives the correct expected value under ‘summation (XY)’ because that is just the probability weighted average, which is the definition of expected value. You could do this much faster by just multiplying through.
In summary, no incremental benefit to using the calculator here. Standard approach seems to be the way to go.

 

[Harrogath]

tickersu wrote:

Harrogath wrote:
2nd STAT (now you have many calculations made automatically, press down button to look for them)
For variance or SD of EPS look for “Var y” and “SD y” respectively.
Hope this helps.
GL

This doesn’t work, because it excludes the probability weightings on each scenario. You need to manually incorporate them. Just run the calculation the “long way”.
[Prob(1)* ((EPS1 - MEANeps)^2)]
Do this for each case, summing, and you have the variance. Take the square root of the variance to arrive at the standard deviation. I got 0.0736 for the variance.

Yeah you right about the variance, weightings were excluded. There is no way to solve it with the Texas. Sorry

 

[S2000magician]

Harrogath wrote:

tickersu wrote:

Harrogath wrote:2nd STAT (now you have many calculations made automatically, press down button to look for them)
For variance or SD of EPS look for “Var y” and “SD y” respectively.
Hope this helps.
GL

This doesn’t work, because it excludes the probability weightings on each scenario. You need to manually incorporate them. Just run the calculation the “long way”.
[Prob(1)* ((EPS1 - MEANeps)^2)]
Do this for each case, summing, and you have the variance. Take the square root of the variance to arrive at the standard deviation. I got 0.0736 for the variance.

Yeah you right about the variance, weightings were excluded. There is no way short-cut to solve it with the Texas. Sorry

Fixed that for you.

 

[Officialmax90]

Thanks Guys, im trying to stretch the caabilities of the Texas BA, i have now learnt the long way anyway.

 

[tickersu]

Officialmax90 wrote:
Thanks Guys, im trying to stretch the caabilities of the Texas BA, i have now learnt the long way anyway.

This will help you in time. Most people don’t gain a strong understanding of anything by using shortcuts. You’ll be thankful you know the long way when you run into trouble with a shortcut. A (financial) calculator should make things easier for you, but it shouldn’t be a crutch– the long way will be your friend forever (and can help you understand concepts and relationships between variables).

 

[Harrogath]

S2000magician wrote:

Harrogath wrote:

tickersu wrote:

Harrogath wrote:2nd STAT (now you have many calculations made automatically, press down button to look for them)
For variance or SD of EPS look for “Var y” and “SD y” respectively.
Hope this helps.
GL

This doesn’t work, because it excludes the probability weightings on each scenario. You need to manually incorporate them. Just run the calculation the “long way”.
[Prob(1)* ((EPS1 - MEANeps)^2)]
Do this for each case, summing, and you have the variance. Take the square root of the variance to arrive at the standard deviation. I got 0.0736 for the variance.

Yeah you right about the variance, weightings were excluded. There is no way short-cut to solve it with the Texas. Sorry

Fixed that for you.

Thanks! My english is not as accurate as I want some times

 

[Harrogath]

tickersu wrote:

Officialmax90 wrote:
Thanks Guys, im trying to stretch the caabilities of the Texas BA, i have now learnt the long way anyway.

This will help you in time. Most people don’t gain a strong understanding of anything by using shortcuts. You’ll be thankful you know the long way when you run into trouble with a shortcut. A (financial) calculator should make things easier for you, but it shouldn’t be a crutch– the long way will be your friend forever (and can help you understand concepts and relationships between variables).

+1

 

[breadmaker]

In STATS mode, for 1-V, the calculator expects your EPS as X and the frequency (in whole numbers) for Y:
2nd DATA
2nd CLR WORK
2nd DATA
X01 1.8 ENTER Y01 10 ENTER
X02 1.6 ENTER Y02 20 ENTER
X03 1.2 ENTER Y03 40 ENTER
X04 1.0 ENTER Y04 30 ENTER
2nd QUIT
2nd STAT
1-V
Display: n = 100, Xbar = 1.28, Sx = 0.27266, sigma x = 0.27129

 

[tickersu]

breadmaker wrote:
In STATS mode, for 1-V, the calculator expects your EPS as X and the frequency (in whole numbers) for Y:
2nd DATA
2nd CLR WORK
2nd DATA
X01 1.8 ENTER Y01 10 ENTER
X02 1.6 ENTER Y02 20 ENTER
X03 1.2 ENTER Y03 40 ENTER
X04 1.0 ENTER Y04 30 ENTER
2nd QUIT
2nd STAT
1-V
Display: n = 100, Xbar = 1.28, Sx = 0.27266, sigma x = 0.27129

The Y-var can act as the absolute frequency of the X-var in 1-var stats mode? Never knew that!