Question

In a sample of n = 6 scores, five of the scores areeach above the mean by one point. Where is thesixth score located relative to the mean?

Answer 1

Step-by-step explanation

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:

`m=(x_1+x_2+x_3+x_4+x_5+x_6)/(n).`

(2) From point 2, we know that:

`x_1=x_2=x_3=x_4=x_5=m+1.`

(3) Replacing this data and n = 6 in the equation of point (1), we have:

`m=(5\cdot(m+1)+x_6)/(6).`

(4) Solving for x₆ the last equation, we get:

`\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}`

We see that the sixth score is located 5 points under the mean.

Answer

The sixth score is located 5 points under the mean.