Standard deviation – example

Hi there, thanks for your question,
First thing to note is that the new CIMA P1 syllabus does not require you to calculate standard deviation from scratch. You need to be able to explain it, understand it and know its relationship to expected value and coefficient of variation. No need to calculate it – however, appreciate your interest in where its derived from.

You have two projects here X and Y . Im unable to paste in a table here – so its difficult to explain the multistage calculation that you need to go through to find standard deviation for each project. Ive attempted to describe it for project X below ( you can calculate yourself for project Y using same method)

Step 1) Find the expected value of the project X ( this is sum of prob x outcomes) This should come to $4000.

Step2) For each outcome in the list compare each to the value to the EV of $4000

Eg – first outcome is $3000 so this is -1000 ( in comparison to the EV) continue down the list. The sum of this list of differences from the EV should total zero.

Step3) For each difference from the EV above then multiply by itself
so first one will be -1000 * -1000 = 1,000,000
Do this for all of the differences you have found in step 2.

Step 4) Multiply each of the answers from step 3 by the original probability for the project outcomes. so for the first line we have
1,000,000 * 0.10 = 100,000
Do this for each line and sum up- this column should equal $300,000

Step5) Take the total from Step 4 and square root it to get the standard deviation of approx $547.72

I hope this explains – it is a bit tricky to show you in words but should follow through if you give it a try.
Many Thanks
Cath