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March 23rd, 2018, 09:32 PM  #1 
Member Joined: Mar 2017 From: Israel Posts: 70 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: 2,197 Thanks: 1152 
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. 
March 24th, 2018, 10:43 AM  #3  
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2  Quote:
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  
Senior Member Joined: Sep 2015 From: USA Posts: 2,197 Thanks: 1152  Quote:
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.  
March 24th, 2018, 01:48 PM  #5 
Global Moderator Joined: May 2007 Posts: 6,641 Thanks: 625 
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 
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2  

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