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March 23rd, 2018, 08:32 PM   #1
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Statistics

Hello

Can you help me please about the next exercise:

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!
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March 23rd, 2018, 10:33 PM   #2
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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.
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March 24th, 2018, 09:43 AM   #3
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Quote:
Originally Posted by romsek View Post
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.
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...
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March 24th, 2018, 09:46 AM   #4
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Quote:
Originally Posted by IlanSherer View Post
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.

Think about it.
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March 24th, 2018, 12:48 PM   #5
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Variances add, so the standard deviation of one slice should be $\sqrt{104}$ unless the slicing is exact.
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March 24th, 2018, 02:08 PM   #6
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Quote:
Originally Posted by mathman View Post
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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