I have 12 balls with mean weight of 500g, and S.D 25g. I have 5 balls with mean weight 200g and S.D

Lucille Cummings

Lucille Cummings

Answered question

2022-06-22

I have 12 balls with mean weight of 500g, and S.D 25g. I have 5 balls with mean weight 200g and S.D 10g. If I combine all of them, is the mean just 8000 17 i.e.
8000 = 500 12 + 200 10
and divided by 17 since there are 17 balls. What is the new S.D.? Is it just
25 12 + 10 5

Answer & Explanation

mar1nerne

mar1nerne

Beginner2022-06-23Added 20 answers

1. For the mean: Yes, this approach is correct, but actually it should be
500 12 + 200 5 = 7000
since in the second sample you have 5 balls and not 10.

2. For the standard deviation. One approach is to use the pooled standard deviation s p which is the root of the pooled variance s p 2 with
s p 2 = ( n 1 1 ) s 1 2 + ( n 2 2 ) s 2 2 ( n 1 1 ) + ( n 2 1 ) = ( 12 1 ) 25 2 + ( 5 1 ) 10 2 ( 12 1 ) + ( 5 1 )

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