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Chapter 2 Describing Variables

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Two basic descriptive statistics for the ... Find Z scores for grouped data on Pres. Obama's handling of the global war on terror, where Mean = 3.30 and N = 158 ... – PowerPoint PPT presentation

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Title: Chapter 2 Describing Variables


1
Chapter 2Describing Variables
  • 2.7 Standardized Scores (Z Scores)

2
Mean and Standard Deviation
Two basic descriptive statistics for the
distribution of a continuous variable with N
observations
Mean (central tendency)
Standard deviation (dispersion)
3
EDUC Years of Schooling
4
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
5
Yi scores into Zi scores
0
5
10
15
20
25
30
35
40
45
Yi
Zi
-1.0
0
.67
-2.0
30
15
6
Change some EDUC Y scores into Z scores
1. What is the Z score for a person with16 years?
2. Find the Z score for a person with 8 years
7
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

8
Find the Z scores for these ungrouped data
First calculate mean standard deviation, then
the Z scores
Y1 6 - _____________________ Y2 4 -
_____________________ Y3 5 -
_____________________ Y4 4 -
_____________________ Y5 3 -
_____________________ Y6 8 -
_____________________
ZY3
ZY6 ________
ZY4 ________
ZY8 ________
9
Find Z scores for grouped data on Pres. Obamas
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 ___________________________ Go
od 3 40
___________________________ Excellent
4 88 ___________________________
10
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
11
Calculate variance std. dev. for 10 scores
2 - _______ _______ 3 -
_______ _______ 3 -
_______ _______ 4 - _______
_______ 5 - _______ _______ 5
- _______ _______ 6 -
_______ _______ 7 - _______
_______ 7 - _______
_______ 8 - _______ _______
12
Find All the Z Scores
(2 - ) / _______ _______ (3
- ) / _______ _______ (3 -
) / _______ _______ (4 - ) /
_______ _______ (5 - ) / _______
_______ (5 - ) / _______
_______ (6 - ) / _______
_______ (7 - ) / _______
_______ (7 - ) / _______
_______ (8 - ) / _______ _______
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