The mean of a dataset is the sum of all data elements divided by the count of the elements.
The location of the 6th score relative to the mean is 5 points below the mean
Let:
[tex]\bar x \to[/tex] Mean
[tex]a \to[/tex] 5 scores
[tex]b \to[/tex] 6th scores
Given that:
[tex]n = 6[/tex]
The 5 scores that are 1 above the mean implies that:
[tex]a = \bar x + 1[/tex]
The mean of a dataset is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x =\frac{5a + b}{6}[/tex]
[tex]\bar x =\frac{5(\bar x + 1) + b}{6}[/tex]
Open brackets
[tex]\bar x =\frac{5\bar x + 5 + b}{6}[/tex]
Multiply both sides by 6
[tex]6\bar x =5\bar x + 5 + b[/tex]
Make b the subject
[tex]b = 6\bar x -5\bar x - 5[/tex]
[tex]b = \bar x - 5[/tex]
This means that the 6th score is 5 points below the mean
Read more about mean at:
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