A population of N =16 scores has a mean of p = 20, After one score is removed from the population, the new mean is found to be μ=19. What is the value of ine score that was removed? (Hint: Compare the val- ues for X before and after the score was removed.)

A population of N =16 scores has a mean of p = 20, After one score is removed from the population, the new mean is found to be μ=19. What is the value of ine score that was removed? (Hint: Compare the val- ues for X before and after the score was removed.)

Question
A population of N =16 scores has a mean of p = 20, After one score is removed from the population, the new mean is found to be \(\displaystyleμ={19}\). What is the value of ine score that was removed? (Hint: Compare the val- ues for X before and after the score was removed.)

Answers (1)

2020-10-28
Let X1, X2,..., X16 be the starting population. We are remowing X16 from this population to obtain the second population.
Thus, the first mean is
PSK((Σ^16)/16)Xi)=20->Σ16Xi=320 i=1 i=1ZSK
The second mean is
PSK((Σ^15)/15)Xi)=19->Σ16Xi=285 i=1 i=1ZSK
From (1) we get that
PSKΣ^15X1+X16=320 i=1ZSK
Plug (2) into the above equation:
\(\displaystyle{285}+{X}{16}={320}\to{X}{16}={35}\)
0

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