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 IlanSherer March 23rd, 2018 08:32 PM

Statistics

Hello :)

The average weight of the cakes is 750 grams, and the standard deviation is 25 grams.
Each cake is divided into 6 slices of equal size, and each slice is added exactly 5 grams of cherry.
What is the average weight and standard deviation of a slice of cake?

I found that the average is 130 (If I'm not mistaken), because:
750/6=125
125+5=130
About standard deviation I'm not sure... I used the data to find the standard deviation, but I got a minus in the root (no solution).
And i don't think the value is (25/6)+5.

Thanks! :)

 romsek March 23rd, 2018 10:33 PM

your calculation of the average is correct.

The standard deviation will be $\dfrac{25}{6}$ as adding the exact weight of the cherry has no effect on the standard deviation.

 IlanSherer March 24th, 2018 09:43 AM

Quote:
 Originally Posted by romsek (Post 590662) your calculation of the average is correct. The standard deviation will be $\dfrac{25}{6}$ as adding the exact weight of the cherry has no effect on the standard deviation.
But why the standard devation is only 25/6? I mean, why I'm not supposed to add 5 grams? I don't really get it...

 romsek March 24th, 2018 09:46 AM

Quote:
 Originally Posted by IlanSherer (Post 590701) Thanks for answering :) But why the standard devation is only 25/6? I mean, why I'm not supposed to add 5 grams? I don't really get it...
standard deviation is a measurement of the spread of a probability distribution.

When you add an exactly known quantity to a random variable you simply translate it's mean value. The spread doesn't change any.

 mathman March 24th, 2018 12:48 PM

Variances add, so the standard deviation of one slice should be $\sqrt{104}$ unless the slicing is exact.

 IlanSherer March 24th, 2018 02:08 PM

Quote:
 Originally Posted by mathman (Post 590709) Variances add, so the standard deviation of one slice should be $\sqrt{104}$ unless the slicing is exact.
"Each cake is divided into 6 slices of equal size", so I think the slicing is exact.

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