From the statement, we have a sample with:
0. n = 6 scores,
,1. five of the scores are each above the mean by one point.
We define the mean as m.
(1) The mean is given by:
[tex]m=\frac{x_1+x_2+x_3+x_4+x_5+x_6}{n}.[/tex](2) From point 2, we know that:
[tex]x_1=x_2=x_3=x_4=x_5=m+1.[/tex](3) Replacing this data and n = 6 in the equation of point (1), we have:
[tex]m=\frac{5\cdot(m+1)+x_6}{6}.[/tex](4) Solving for x₆ the last equation, we get:
[tex]\begin{gathered} 6m=5\cdot(m+1)+x_6, \\ 6m=5m+5+x_6, \\ x_6=6m-5m-5, \\ x_6=m-5. \end{gathered}[/tex]We see that the sixth score is located 5 points under the mean.
AnswerThe sixth score is located 5 points under the mean.
