What is the difference between 1/N sum (y_i)/(x_i) and sum (overliney)/(overlinex)

charmbraqdy

charmbraqdy

Answered question

2022-11-04

What is the difference between 1 N y i x i and y ¯ x ¯
I have a data set and I was looking at the population ratio and trying to estimate it using different methods. I was expecting eq1 and eq2 to be different but was very surprised that it was by a factor of almost 3x. I was just wondering why it was so different, is it partly due to n cancelling on eq2. Any explanation would be appreciated.

Answer & Explanation

Raven Hawkins

Raven Hawkins

Beginner2022-11-05Added 19 answers

Explanation:
Say x i = i, y i = n + 1 i, for 1 i n. The sum i y i / x i = i ( n + 1 i ) / i = ( n + 1 ) H n n, y ¯ / x ¯ = 1, quite different (here H n = 1 k n 1 / k is the harmonic numbers).

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