Question

1. Liv attends “Happy Days” preschool. The preschool ran assessments on the children’s motor skills (such as ability to tie a shoe), social skills (such as sharing and saying “please” and “thank you”), and school readiness (such as knowing ABCs and basic counting). The motor skills test has a class mean of 6 with a standard deviation of 1, the social skills test has a class mean of 10 with a standard deviation of 2, and the school readiness test has a mean of 16 with a standard deviation of 4. Liv’s parents are given a report that indicates that her z score for motor skills is –1.11, for social skills it is 0.25, and for school readiness it is 0.

a. The parents do not know what z scores are. Clearly define for them what a z score measures and the advantages of using z scores compared to raw scores.

b. What does a z score = –1.11 mean? A z score of 0.25? A z score of 0?

c. What are Liv’s raw scores on each test?

Answer 1

a) Z scores are calculated by normalizing the raw scores with mean and standard deviation i.e .

* A z score measures the distance of the raw score from the mean in terms of number of standard deviations

Advantages of z scores:

* They help in easily interpreting the raw scores

* The probabilities can be easily calculated with z scores by using a single z table

* They ease computation by transforming very large raw scores to smaller z scores

b) A z score of -1.11 means the corresponding raw score is 1.11 times the standard deviation below the mean

A z score of 0.25 means the corresponding raw score is 0.25 times the standard deviation above the mean

A z score of 0 means the corresponding raw score is equal to the mean

c) The motor skills test has a class mean of 6 with a standard deviation of 1.

The social skills test has a class mean of 10 with a standard deviation of 2.

The school readiness test has a mean of 16 with a standard deviation of 4

Liv’s score for motor skills = 6-1.11*1 = 4.89

Liv’s score for social skills = 10+0.25*2 = 10.5

Liv’s score for school readiness = 16+0*4 = 16