Z+score

===Z score gives the precise percentage between 0 and the Z point in a Normal Curve. It is used when you want to find out the proportion above or below a certain point (the Z score) or between two points.===



How we find the Z score:

where X = our chosen point, Χ = sample mean (average) (See Measures of Central Tendency), and S = Standard Deviation.

The + or - sign of the Z show us whether the score is above or below the mean. The numerical value indicate the distance from the mean.

**Find the proportion. Try it out!**
Age in EDS115:
 * || Mean  ||  Stdev  ||  N  ||
 * Female ||  26  ||  5  ||  27  ||
 * Male ||  26  ||  3  ||  8  ||

Find proportion //below// certain point, //above// the mean:
1. Convert score to Z score. 2. Find area between mean and Z (b). 3. Add 0,5 (= the whole area below the mean, 50% of total)

Ex: Female, 28 years. How big proportion of class is younger than I am?

(28-26) / 5 ≈ 0,67 0,67 = 0,2486 0,2486 + 0,5 = 0,7486 0,7486 = 74,86% ≈ 75%

Find proportion //below// certain point, //below// the mean:
1. Convert score to Z score. 2. Find "area beyond Z" (c).

Ex: Female, 24 years. How big proportion of class is younger than I am?

(24-26) / 5 ≈ 0,67 0,67 = 0,2514 0,2514 = 25,14% ≈ 25%

Find proportion //above// certain point//, below// the mean:
1. Convert score to Z score. 2. Find area between mean and Z (b). 3. Add 0,5 (= the whole area above the mean, 50% of total)

Ex: Male, 23 years. How big proportion of class is older than I am?

(23-26) / 3 = 1 1 = 0,3413 0,3413 + 0,5 = 0,8413 0,8413 = 84,13% ≈ 84%

Find proportion //above// certain point, above the mean:
1. Convert score to Z score. 2. Find "area beyond Z" (c).

Ex: Male, 30 years. How big proportion of class is older than I am?

(30-26) / 3 ≈ 1,34 1,34 = 0,0901 0,0901 = 9,01% ≈ 9%

Find proportion between two points, the higher above mean, the lower below:
1. Convert score to Z score at both points 2. Find areas between mean and Z points. 3. Add the two values.

Ex. How big proportion of the class' females are between 25 and 29 years?

(25-26) / 5 = 0,2 0,2 = 0,0793

(26-29) / 5 = 0,6 0,6 = 0,2743

0,2743+0,0793 = 0,3536 = 35,36% ≈ 35%

35% of the class is between 25 and 29 years old.