Download Unit 6: Descriptive Statistics

Introduction to Using
Statistical Analyses
Measures
of Central Tendency
(done . . .for now)
Measures of Variability
Writing
Using the Standard Normal Curve
A Reminder of the Way We Note Things:
Our Shorthand
X


N
i
A Reminder of the Way We Note Things:
Our Shorthand
X


N
i
A Reminder of the Way We Note Things:
Our Shorthand
X


N
i
A Reminder of the Way We Note Things:
Our Shorthand
X


N
i
A Reminder of the Way We Note Things:
Our Shorthand
X


N
i
Population and Sample Means
X


N
i
Population and Sample Means
X


i
N
X
X
 i
n
Introduction to Using
Statistical Analyses
Measures
of Central Tendency
(done . . .for now)
Measures
of Variability
Writing
Using
the Standard Normal Curve
Assessing Dispersion by
Looking at Spread
Data
2
5
8
Mean = 5
Assessing Dispersion by
Looking at Spread
Data
2
5
8
Mean = 5
How far from the
mean are the data?
Starting to Assess the Variance
s
2
X


2 -5 =-3
5 -5 = 0
8 -5 = 3
i
X
n 1

2
A Formula to Assess the
Variance
s
2
X


i
X
n 1
2 -5 =-3
9
5 -5 = 0
0
8 -5 = 3
9

2
A Formula to Assess the
Variance
s
2
X


9
5 -5 = 0
0
8 -5 = 3
X  X

s 
9
18
i
n 1
X
n 1
2 -5 =-3
2
i
2
=

2
A Formula to Assess the
Variance
s
2
X


9
5 -5 = 0
0
8 -5 = 3
X  X

s 
9
18
i
n 1
X

n 1
2 -5 =-3
2
i
2
2
=
9
2 18
A Formula to Assess the
Variance
s
2
X


9
5 -5 = 0
0
2
i
n 1
X

n 1
2 -5 =-3
8 -5 = 3
X  X

s 
i
2
2
=
9
18
9
2 18
THE VARIANCE
Sample and Population
Standard Deviations
s
 
 X
i
 X

2
n 1
 X
i
 
N

2
SAMPLE AND POPULATION TERMS
Sample
Population

SAMPLE AND POPULATION TERMS



n
Sample
Mean
Population
X

XX  
i
i
N
2

SAMPLE AND POPULATION TERMS



Sample
Mean
Variance
Population
X
2

XX i  


X 
X  X
n


2
s 
s 
i
2
2
N n
1
i
2
i

n 1

SAMPLE AND POPULATION TERMS



Sample
Mean
Variance
Standard
Deviation
Population
X
2

XX i   2



X

X

X
n


i
i
2
2
2
s 2 
s N 


X

X
n

1
n

1

i
2
2
 
s 
i
n 1
Introduction to Using
Statistical Analyses
Measures
of Central Tendency
(done . . .for now)
Measures of Variability
Writing
Using
the Standard Normal Curve
Introduction to Using
Statistical Analyses
Measures
of Central Tendency
(done . . .for now)
Measures of Variability
Writing
Using
Curve
the Standard Normal
Standard Normal Curve
Standard Normal Curve


X



2
-3
i
N
=0
= 1 
+3

z Scores when Data Do Not Already Have a Mean
of 0 and a Standard Deviation of 1
z
X 

z Scores when Data Do Not Already Have a Mean
of 0 and a Standard Deviation of 1
z
or
X 

XX
z
s
Areas under the Standard
Normal Curve
z = -1.67
z=1
0
Areas under the
Standard Normal Curve
z = -1.75
z = 1.75
0
Areas under the
Standard Normal Curve
z=1
0
Correlations
Correlation Example
Speaking Skill
Writing Skill
X
Y
1
3
2
4
3
7
4
5
5
6
Correlation Chart
*
7
6
*
5
4
Writing skill
3
*
2
*
*
1
0
0
1
2
3
Speaking Skill
4
5
Correlation Chart
*
7
6
*
5
4
Writing skill
3
*
2
*
*
1
0
0
1
2
3
Speaking Skill
4
5
Correlation Chart
*
7
6
*
5
4
Writing skill
3
*
2
*
*
1
0
0
1
2
3
Speaking Skill
4
5
Correlation Example Using
z scores
Speaking Skill
Writing Skill
X
Y
Zx
Zy
1
- 1.27
3 - 1.27
2
- .63
4 - .63
3
0
7
1.27
4
.63
5
0
5
1.27
6
.63
Correlation Example Using
z scores
Speaking Skill
Writing Skill
X
Y
Zx
Zy
Zx * Zy
1
- 1.27
3 - 1.27
1.61
2
- .63
4 - .63
.4
3
0
7
1.27
0
4
.63
5
0
0
5
1.27
6
.63
.8
Correlation Example Using
z scores
Speaking Skill
Writing Skill
X
Y
Zx
Zy
Zx * Zy
1
- 1.27
3 - 1.27
1.61
2
- .63
4 - .63
.4
3
0
7
1.27
0
4
.63
5
0
0
5
1.27
6
.63
.8
SUM = _ 2.81 __
n-1 = 4
Correlation Example Using
z scores
Speaking Skill
Writing Skill
X
Y
Zx
Zy
Zx * Zy
1
- 1.27
3 - 1.27
1.61
2
- .63
4 - .63
.4
3
0
7
1.27
0
4
.63
5
0
0
5
1.27
6
.63
.8
SUM = _ 2.81 __
n-1 = 4
=.70
Correlation Example
Speaking Skill
X
XX
Writing Skill
Y
Y Y
1
-2
3 -2
2
-1
4 -1
3
0
7
2
4
1
5
0
5
2
6
1
Correlation Example
Speaking Skill
X
XX
Writing Skill
Y
Y Y
XX
*
1
-2
3 -2
4
2
-1
4 -1
1
3
0
7
2
0
4
1
5
0
0
5
2
6
1
2
Y Y
Correlation Example
Speaking Skill
X
XX
Writing Skill
Y
Y Y
XX
*
1
-2
3 -2
4
2
-1
4 -1
1
3
0
7
2
0
4
1
5
0
0
5
2
6
1
2
 X  X  Y  Y 
Y Y
=7
Correlation Example
Speaking Skill
X
XX
Writing Skill
Y
Y Y
XX
*
1
-2
3 -2
4
2
-1
4 -1
1
3
0
7
2
0
4
1
5
0
0
5
2
6
1
2
 X  X  Y  Y 
n-1
Y Y
=7
=4
Correlation Computation
7
 1. 75
4
r
s X * sY
Correlation Computation
7
 1. 75
4
r
s X * sY
Correlation Computation
7
 1. 75
4
r
s X * sY
1. 75
r
1.58 *1.58
1. 75
r
. 70
2.5
Correlation Computation
7
 1. 75
4
r
s X * sY
1. 75
r
1.58 *1.58
1. 75
r
. 70
2.5
Correlation Computation
7
 1. 75
4
r
s X * sY
1. 75
r
1.58 *1.58
1. 75
r
. 70
2.5