CALCULATING THE STANDARD DEVIATIONS FOR DATA SET 1 AND DATA 2 ASSIGNMENT

EXAMPLE FOR TRANSFORMING SCORES INTO STANDARD SCORES

First, copy the Data Set 1 distribution under score. Then, use the mean and standard deviation of Data Set 1 to transform its distribution into the following standard scores. (See formulae below)

Score z-score T-score Deviation-IQ SAT

1. 100 1.29 62.9 ? ?

2. 98

3. 96

4. 94

5. 88

6. 87

7. 82

Formulae for Transforming Raw Score into Standard Score

Z-Score z = (X– Mean)/SD = (Score minus Mean divided by standard deviation)

T-Score T =z (10) + 50 = (1.29 x 10) + 50 =

Deviation-IQ Score IQ =z (15) + 100

SAT Score SAT =z (100) + 500

The computation of the above seven (7) distribution of scores yielded:

Mean = 92.14; Variance = 37.30; Standard Deviation = 6.11

To derive the Z score (see formula above):

Z = (100 – 92.14) divided (/) by Standard Deviation (6.11) = (7.86/6.11) = 1.29

NOTE:

1. Before working on the Assignment, complete the above distribution. It will help you to know what to do.

2. By substitution you solve for the Standard Scores.

3. Should you have any question, contact the lecturer at [email protected] .