SOLUTION: the mean of 5 observations is 20.including one new observation,the mean is 25.find the newly included observation

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Question 830238: the mean of 5 observations is 20.including one new observation,the mean is 25.find the newly included observation
Answer by jim_thompson5910(35256) About Me  (Show Source):
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the mean of 5 observations is 20.including one new observation,the mean is 25.find the newly included observation
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Let S = sum of the first 5 observations

Since "the mean of 5 observations is 20", this means that S/5 = 20

S/5 = 20

S = 20*5 ... Multiply both sides by 5.

S = 100

So the sum of the first 5 observations is 100.

Now let x = measure of the newly included observation

The mean, call it m, is equal to the sum of the 6 items divided by 6. Or put another way, it's equal to the sum of the first five items (S) and that new sixth observation (x). Then you divide by 6. This gives the mean m. So,

%28S%2Bx%29%2F6+=+m

%28S%2Bx%29%2F6+=+25 Plug in that new mean m = 25

%28100%2Bx%29%2F6+=+25 Plug in S = 100

100%2Bx+=+25%2A6 Multiply both sides by 6.

100%2Bx+=+150

x+=+150-100

x+=+50

Therefore, the newly included observation is 50, which is the final answer.