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PRED 35 4 TEACH. PROBILITY & STATIS. FOR PRIMARY MATH

PRED 35 4 TEACH. PROBILITY & STATIS. FOR PRIMARY MATH. Lesson 4 Z-SCORES. CORRECTIONS. Having gap in the distribution Real limits Grouped-frequency distributions. CORRECTIONS. Real Limits Assigment 2,5  38,46% 3 -> 42,3% 46,15% ---  ??. CORRECTIONS.

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PRED 35 4 TEACH. PROBILITY & STATIS. FOR PRIMARY MATH

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

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

  3. CORRECTIONS Real Limits Assigment 2,5  38,46% 3 -> 42,3% 46,15% --- ??

  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

  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. • The sign tells whether the score is located above (+) or below (-) the mean, and • 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 Find a) 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. Probability Evaluating treatment effects Measuring relationship Why are z-scores important?

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