# Standard scores, measures of variability, & norms

First, explain the purpose of transforming raw scores into standard scores. Describe what "normal distribution" means.

Next, briefly describe measures of variability, and explain how they might help you understand assessment data.

Finally, describe the function of norms in psychological assessment. Include the following in your discussion:

Percentile ranks

Age norms

Grade norms

https://brainmass.com/statistics/normal-distribution/standard-scores-measures-of-variability-norms-323956

#### Solution Preview

1. We transform raw scores into standard scores so that we can compare scores from different scales. Imagine you wanted to know which was warmer: 20 degrees Celsius or 10 degrees Fahrenheit. How would you go about answering that? You'd have to convert one temperature to the other scale so that you could compare them both on the same scale. When we convert raw scores to standard scores, that's what we're doing - we're putting them on the same scale of measurement. Standard scores are also useful because they give us some quick information, especially when the standard scores are z scores. Since a z score represents a standard deviation, we immediately know whether the raw score we've observed is quite typical (e.g. z=1.5) or quite rare (e.g. z=3.5).

2. The normal distribution is a bell-shaped curve (the most common scores occur in the middle and the curve lowers as you move further from the middle). It is ...

#### Solution Summary

Explains how to calculate standard scores, meaures of variability, and the use of norms in psychological testing.