My Math Forum Statistics

 March 23rd, 2018, 09:32 PM #1 Member   Joined: Mar 2017 From: Israel Posts: 81 Thanks: 2 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!
 March 23rd, 2018, 11:33 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,317 Thanks: 1230 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 from IlanSherer
March 24th, 2018, 10:43 AM   #3
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Quote:
 Originally Posted by romsek 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...

March 24th, 2018, 10:46 AM   #4
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Quote:
 Originally Posted by IlanSherer 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.

 March 24th, 2018, 01:48 PM #5 Global Moderator   Joined: May 2007 Posts: 6,684 Thanks: 659 Variances add, so the standard deviation of one slice should be $\sqrt{104}$ unless the slicing is exact.
March 24th, 2018, 03:08 PM   #6
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Quote:
 Originally Posted by mathman 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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