# Given the data  9, 5, 10, 7, 9, 10, 11, 8, 12, 7, 6, and 9 , what would be the raw scores be that correspond to the following:  (a) z = +1.22 (b) z = -2.0.

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to use the following formula, such that:

`z = (x - mu)/sigma` => x = z*sigma + mu

x represents the raw score

`mu` represents the mean

`sigma` represents the standard deviation

You need to evaluate the mean using the formula, such that:

`mu = (9+5+10+7+9+10+11+8+12+7+6+9)/12 => mu = 8.583`

You need to evaluate the standard deviation using the following formula, such that:

`sigma = sqrt((3(9-8.583)^2 + (5 - 8.583)^2 + 2(10-8.583)^2 + 2(7 - 8.583)^2 + (11 - 8.583)^2 + (8 - 8.583)^2 + (12 - 8.583)^2 + (6 - 8.583)^2)/(12 - 1))`

`sigma = 2.065`

Replacing the z score 1.22, 2.065 for standard deviation `sigma` and 8.583 for the mean `mu` in `x = z*sigma + mu` , yields:

`x = 1.22*2.065 + 8.583 => x = 11.102`

Hence, evaluating the raw score for the z score `z = +1.22` yields `x = 11.102.`

b) You need to evaluate the raw score for the z score z = -2.0, such that:

`x = z*sigma + mu = > x = -2.0*2.065 + 8.583 => x = 4.453`

Hence, evaluating the raw score for the z score `z = -2.0` yields `x = 4.453.`

Sources: