Comparing_Scores

=Comparing Scores on Standardized Tests= //Posted for MATH 623 - Not public at this time.//

The Standard Normal Distribution is used to make comparisons in a ‘unit free” environment. When we are given two different data sets, with different centers and spreads, we need to “normalize” the data so they both have a mean of 0 and a standard deviation of 1. Then, we can make comparisons.
 * Introduction**

Classic questions used in statistics courses follow.

1. David took the SAT in 2013 and scored 687 points (Math portion). His friend Sheila took the ACT in 2010 and scored 31 points (Math portion). Who scored higher?

First, we need to locate the mean and standard deviation for the specific tests. In 2013, the SAT information is N(514, 118) for all students. In 2010, the ACT information is N(21, 5.3) for all students.

Convert both scores to z-scores: z-score David = (687-514)/118= 1.466 z-score Shelia = (31-21)/5.3= 1.887
 * Shelia did a better job on her test than David.**

2. In the same years, respectively, Jerry got an SAT score of 560 points and Kay got a 23 on the ACT. Who scored higher?

Convert both scores to z-scores: z-score Jerry = (543-514)/118 = 0.246 z-score Kay = (23-21)/5.3 = 0.377
 * Answer: Kay scored higher than Jerry.**

3. What would Jerry need to score on the SAT to match Kay’s score of a 23 on the ACT?

Working backwards in the formula, solve for x. z-score Kay = (x-514)/118 0.377 = (x-514)/118 x=558.486 rounded to 559
 * Answer: Jerry would need to get a 559.**

4. Would it make a difference if we used the statistics that are specific for a specific demographic (sex or ethnicity)? Why?

Spreadsheet in TinkerPlots - You can always use a calculator.