Question

A psychologist is working with a large group of schizophrenic patients and would like to divide them up into groups in order to make his work easier. He feels that it is bet to divide them up by symptom severity in order to better serve the patients. He gives each patient a battery of tests to evaluate which group each patient should be in. He then gives them one single composite score that he labels symptom severity. He notices that the scores are normally distributed, so he decides to divide the distribution into 3rds based on z-scores. The mean of the distribution is 32.45 with a standard deviation of 5.43. He wants to break the group up into a lower 3rd, middle, 3rd and upper 3rd. What raw scores would he use as the dividing point between the three groups? (HINT: there should be two scores)

Answer 1

= 32.45

= 5.43

First Quartile = Q1 = area from mid value to Z on LHS = 0.25

Table of Area Under Standard Normal Curve gives Z = - 0.675

So,

Z = - 0.675 = (X - 32.45)/5.43

So,

X = 32.45 - (0.675 X 5.43)

= 32.45 - 3.6653

= 28.7845

Third Quartile = Q3 = area from mid value to Z on RHS = 0.25

Table of Area Under Standard Normal Curve gives Z = 0.675

So,

Z = 0.675 = (X - 32.45)/5.43

So,

X = 32.45 + (0.675 X 5.43)

= 32.45 + 3.6653

= 36.1153

So,

The raw scores would he use as the dividing point between the three groups are:

28.7845 and 36.1153