Chapter 2 Describing Variables 2 7 Standardized Scores

Chapter 2 Describing Variables 2. 7 Standardized Scores (Z Scores) 1/25/2022

Mean and Standard Deviation Two basic descriptive statistics for the distribution of a continuous variable with N observations: Mean (central tendency): Standard deviation (dispersion): 1/25/2022

EDUC Years of Schooling 1/25/2022

Standardized Scores (Z Scores) Transform each score in the frequency distribution of a continuous Y-variable into a standard or Z score: (1) from Yi subtract the mean (= deviation di) (2) divide case i deviation by the standard deviation Z scores can be positive or negative, indicating the number of standard deviation units that Yi lies above or below the distribution mean 1/25/2022

Yi scores into Zi scores Yi Zi 0 -2. 0 5 10 15 20 25 -1. 0 0 = 30 1/25/2022 30 35 40 45 +. 67 = 15

Change some EDUC Y scores into Z scores: 1. What is the Z score for a person with 16 years? 2. Find the Z score for a person with 8 years: 1/25/2022

Now change some EDUC Z scores into Y scores: What years of EDUC separate two persons at the upper & lower limits of the range Z = ± 2. 2 standard deviations? • Find upper limit of range, Z = +2. 20 std. dev. units : • Find lower limit of range, Z = -2. 20 std. dev. units : 1/25/2022

Find the Z scores for these ungrouped data: First calculate mean & standard deviation, then the Z scores Y 1: 6 - ___________ Y 2: 4 - ___________ Y 3: 5 - ___________ Y 4: 4 - ___________ Y 5: 3 - ___________ Y 6: 8 - ___________ ZY=3 = ZY=6 = ____ ZY=4 = ____ ZY=8 = ____ 1/25/2022

Find Z scores for grouped data on Pres. Obama’s handling of the global war on terror, where Mean = 3. 30 and N = 158 Rating Yi fi (di)2(fi) Poor 1 10 ______________ Fair 2 20 ______________ Good 3 40 ______________ Excellent 4 88 ______________ 1/25/2022

Calculate the mean for ungrouped data 1 2 2 3 3 3 4 4 5 5 6 5 7 6 8 7 9 7 10 8 1/25/2022

Calculate variance & std. dev. for 10 scores 2 - = _______ 3 - = _______ 4 - = _______ 5 - = _______ 6 - = _______ 7 - = _______ 8 - = _______ 1/25/2022