The discussion revolves around calculating the variance of the average weight of plums in a pack, given the average weight and standard deviation of individual plums. The original poster presents their calculations and seeks clarification on their approach.
Participants have engaged in clarifying the calculations and discussing the assumptions regarding the independence of the plum weights. Some guidance has been offered regarding the importance of writing out explanations, and there is acknowledgment of the potential correlation in the weights of the plums based on selection methods.
The original problem statement does not specify whether the weights of the plums are independent, which is a critical assumption for the variance calculation. This aspect is under discussion among participants.
I can easily guess the answers to these questions, but that's not the point. By writing it out, you clarify things in your own mind.CryptoMath said:Variance/n
Average_Total: as in the average of all the 14 plums.andrewkirk said:You'll find it easier to understand if you write sentences around your formulas, explaining what they represent.
For instance, what is 'Average_Total' and why did you write
I can easily guess the answers to these questions, but that's not the point. By writing it out, you clarify things in your own mind.
Writing explanatory sentences helps it fit together in a logical manner in your mind, rather than just being a jumbled bunch of formulas that you try to commit to memory, hoping to use the right one at the right time.
I got this one resolved it is simply that:andrewkirk said:You'll find it easier to understand if you write sentences around your formulas, explaining what they represent.
For instance, what is 'Average_Total' and why did you write
I can easily guess the answers to these questions, but that's not the point. By writing it out, you clarify things in your own mind.
Writing explanatory sentences helps it fit together in a logical manner in your mind, rather than just being a jumbled bunch of formulas that you try to commit to memory, hoping to use the right one at the right time.
I have an other exercise, may you help me with that one please ?andrewkirk said:That's right, the formula that the variance of a sum of independent random variables is the sum of the variances is true regardless of distribution.
BTW, the problem statement omitted to say that the weight of plums in the pack is independent, which is essential to obtaining the solution. In practice, that may not be the case, depending on how the sample of 14 was selected. For instance if there is a lot of jostling there will be more larger plums near the top, and smaller near the bottom. So 14 plums selected from near one another would be expected to have correlated sizes.
https://www.physicsforums.com/threads/math-probability-need-to-find-the-variance.857348/andrewkirk said:OK. Post it as a new thread though, unless it's very closely related, to avoid confusing readers..