What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their mom or child how would one go about it?
It's a concept that I have difficulty in articulating - especially when relating variance to risk. I understand it mathematically and can explain it that way too. But when explaining real world phenomena how do you make one understand variance and it's applicability in the 'real world', so to speak.
Let's say we are simulating an investment in a stock using random numbers (rolling a die or using an excel sheet, doesn't matter). We get some 'return on investment' by associating each instance of the random variable to 'some change' in the return. Eg.:
Rolling a 1 implies a change of 0.8 per \$1 in investment, a 5 a change of 1.1 per \$1 and so on.
Now if this simulation is run for about 50 times (or 20 or 100) we will get some values and the final value of the investment. So what does 'variance' actually tell us if we were to calculate it from the above data set? What does one "see" - If the variance turns out to be 1.7654 or 0.88765 or 5.2342 what does this even mean? What did/can I observe about this investment?? What conclusions can I draw - in lay man terms.
Please feel free to augment the question with that for standard deviation too! Although I feel it's 'easier' to understand, but something that would contribute to making it also 'intuitively' clear would be greatly appreciated!