1. PRED 354 TEACH. PROBILITY & STATIS. FOR PRIMARY MATH Lesson 4 Z-SCORES

2. CORRECTIONS 1. Having gap in the distribution 2. Real limits 3. Grouped-frequency distributions

3. CORRECTIONS Real Limits Assigment 2,5  38,46% 3 -> 42,3% 46,15% ---  ?? Xfc% 102 97 82 71 60 5253,84 4046,15 32 2838,46 127,69

4. CORRECTIONS Grouped frequency distribution tables Rule 1. The grouped frequency distribution table should have about 10 class intervals. Rule 2. The width of each interval should be relatively simple number. Rule 3. The bottom score in each class interval should be a multiple of the width. Rule 4. All intervals should be the same width.

5. CORRECTIONS XwidthBottom score 25-3525 15-2515 5-15115

6. Quiz ANNOUNCED IN THE CLASS

7. Z-scores: location of scores and standardized distributions A z-score specifies the precise location of each X value within a distribution. 1. The sign tells whether the score is located above (+) or below (-) the mean, and 2. The number tells the distance between the score and the mean in terms of the number of standard deviations.

8. Z-scores: location of scores and standardized distributions z = (X - µ) / σ EX. The distribution of SAT verbal scores for high school seniors has a mean of µ=500 and a standard deviation of σ=100. He took the SAT and scored 430 on the verbal subtest. Locate his score in the distribution by using a z-score.

9. Z-scores: location of scores and standardized distributions EX. A distribution of exam scores has a mean of 50 and standard deviation of 8. What raw score corresponds to z=-1/2? What is z-score of X=68? PURPOSE: to convert each individual score into a standardized z-score, so that the resulting z-score provides a meaningful description of exact location of the individual score within the distribution.

10. Z-scores: location of scores and standardized distributions Whenever you are working with z-scores, you should imagine or draw a picture similar to this figure. Although you should realize that not all distributions are normal, we will use the normal shape as an example when showing z-scores.

11. Charateristics of a z-scores distribution 1. Shape 2. The mean 3. The standard deviation EX. A population of N=6 scores consists of the following values: 0, 6, 5, 2, 3, 2 Finda) z-scores, b) graphs of the distributions c)means d) σs

12. Using z-scores to make comparisons Suppose, for example, that Ali recevied a score of X=60 on math exam (µ=50, σ=10) and a score of X=56 on biology test (µ=48, σ=4). Which exam score is better? Why is it possible to compare scores from different distributions after each distribution is tranformed into z-scores?

13. Transforming z-scores to a predetermined µ and σ the goal is to create a new standardized distribution that has simple values for the mean and standardized deviation, but does not change any inidividual’s location within the distribution. Ex: An instuctor gives an exam to a physic class. For this exam, the distribution of raw scores has a mean of µ = 57 and σ = 14. The instructor would like to simplify the distribution by tranforming all scores into a new standardized distribution with µ = 50 and σ = 10. What is Ali’s and Veli’s new scores if they took 64 and 43, respectively?

14. Transforming z-scores to a predetermined µ and σ EX: For the following population, Scores: 2, 4, 6, 10, 13 Tranform this distribution for µ=50, σ=20.

15. Why are z-scores important? 1. Probability 2. Evaluating treatment effects 3. Measuring relationship