Question

Which score has a higher relative position, a score of 38 on a test for which = 27 and s = 10, or a score of 262.7 on a test for which = 200 and s = 57?

Answer 1

the first one because it has numbers closer together

Answer 2

Both score has same relative position.

Explanation:

The formula for relative position is

`z=\frac{X-\bar {X}}{s}`

where, X is the value of the data point,
`\bar {X}` is mean, and s is standard deviation.

It is given that a score of 38 on a test for which mean = 27 and s = 10.

`z_1=(38-27)/(10)=1.1`

A score of 262.7 on a test for which mean = 200 and s = 57.

`z_2=(262.7-200)/(57)=1.1`

`z_1=z_2`

Both score has same relative position.