Question

In a sample of n = 6 scores, 5 of the scores are each above the mean by one point. Where is the 6th score located relative to the mean?

Answer 1

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:

$\bar x \to$ Mean

$a \to$ 5 scores

$b \to$ 6th scores

Given that:

$n = 6$

The 5 scores that are 1 above the mean implies that:

$a = \bar x + 1$

The mean of a dataset is calculated using:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x =\frac{5a + b}{6}$

$\bar x =\frac{5(\bar x + 1) + b}{6}$

Open brackets

$\bar x =\frac{5\bar x + 5 + b}{6}$

Multiply both sides by 6

$6\bar x =5\bar x + 5 + b$

Make b the subject

$b = 6\bar x -5\bar x - 5$

$b = \bar x - 5$

This means that the 6th score is 5 points below the mean

Read more about mean at:

brainly.com/question/17060266