Variability as a part of descriptive statistic (Lecture slides mostly in Bahasa Indonesia)

1. PDU 207 STATISTIK DASAR
SEKSI E
SEMESTER GASAL 2016/2017
FAKULTAS PSIKOLOGI / PROGRAM STUDI S1 PSIKOLOGI
Variability
KULIAH V – 05 SEPTEMBER 2016

2. Menguasai teknik-teknik statistika deskriptif dan statistika inferensial,
secara khusus terkait dengan:
• Tujuan umum dilakukannya perhitungan variabilitas, serta perbedaan kumpulan skor
berdasarkan derajat variabilitasnya;
• Konsep dan perhitungan berbagai teknik variabilitas.
Memiliki kemampuan menyampaikan argumentasi dan penalaran
dengan bahasa yang tepat, khususnya berkaitan dengan:
• Pemilihan teknik perhitungan variabilitas yang paling tepat sesuai dengan jenis data
dan tujuan pengukurannya.
One-Day Objectives

3. Introduction to
Variability

4. PDU 207 STATISTIK DASAR 2016 © Ardhiati 4
Usia Saat Pertama Kali
Jatuh Cinta
15 tahun
CENTRAL
TENDENCY

5. PDU 207 STATISTIK DASAR 2016 © Ardhiati 5
Usia Saat Pertama Kali
Jatuh Cinta
15 tahun
VARIABILITY
8 tahun 23 tahun

6. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Variability
6
Variability provides a quantitative measure of
the differences between scores in a distribution
and describes the degree to which the scores
are spread out or clustered together.
THE DEFINITION
(Gravetter & Wallnau, 2012: 104)
15 16 171413
Usia Saat Pertama Kali Berpacaran
(tahun)
15 19 23118
Usia Saat Pertama Kali Jatuh Cinta
(tahun)

7. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Variability
7
SERVES TWO PURPOSES
(Gravetter & Wallnau, 2012: 105)
1 Describes the
distribution
2 Measures how well
an individual score (or
group of scores) represents
the entire distribution
158 231713
15
8
23

8. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Variability
8
THE MEASURES
VARIABILITY
THE RANGE
STANDARD
DEVIATION VARIANCE

9. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Variability
9
THE MEASURES
VARIABILITY
THE
INTERQUARTILE
RANGE
THE RANGE
STANDARD
DEVIATION VARIANCE

10. Measurement of
Variability

11. PDU 207 STATISTIK DASAR 2016 © Ardhiati
The Range
11
The distance covered by the scores in a distribution,
from the smallest score to the largest score.
(Gravetter & Wallnau, 2012: 106)
range = Xmax - Xmin + 1
= URL for Xmax - LRL for Xmin
11 14 13 13 14 14 23 13 15 14
8 15 17 15 14 15 16 16 14 13
Usia Saat
Pertama Kali
Jatuh Cinta
it is completely
determined by the two
extreme values
TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS
COUNT vs MEASURE ☐ COUNT ☐ MEASURE
MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO
ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH
✓
✓
✓
✓ ✓ ✓
✓

12. PDU 207 STATISTIK DASAR 2016 © Ardhiati
The Interquartile Range
12
The distance covered by the middle 50% of the distribution
(Q3 - Q1).
14 15 16 17 18 19 20 21 22 231312111098
1
2
3
4
5
6
Usia Saat
Pertama Kali
Jatuh Cinta
TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS
COUNT vs MEASURE ☐ COUNT ☐ MEASURE
MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO
ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH

13. PDU 207 STATISTIK DASAR 2016 © Ardhiati
The Interquartile Range
13
The distance covered by the middle 50% of the distribution
(Q3 - Q1).
14 15 16 17 18 19 20 21 22 231312111098
1
2
3
4
5
6
Bottom 25% Top 25%
Q1 = 13,25 Q3 = 15,25
Interquartile Range
= Q3 - Q1
= 2
TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS
COUNT vs MEASURE ☐ COUNT ☐ MEASURE
MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO
ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH
✓
✓
✓
✓ ✓ ✓
✓
Usia Saat
Pertama Kali
Jatuh Cinta

14. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Standard Deviation & Variance
14
The average distance from the mean.
(Gravetter & Wallnau, 2012: 106-114)
FOR POPULATION
X X - μ (X - μ)2
8 -6,35 40,32
11 -3,35 11,22
13 -1,35 1,82
13 -1,35 1,82
13 -1,35 1,82
13 -1,35 1,82
14 -0,35 0,12
14 -0,35 0,12
14 -0,35 0,12
14 -0,35 0,12
14 -0,35 0,12
14 -0,35 0,12
15 0,65 0,42
15 0,65 0,42
15 0,65 0,42
15 0,65 0,42
16 1,65 2,72
16 1,65 2,72
17 2,65 7,02
23 8,65 74,82
find the deviation
(distance from the mean)
for each score
square each deviation
find the average
of the squared deviations
take the square root
of the variance
STANDARD
DEVIATION
VARIANCE 7,43
2,73
μ = 14,35 SS = 148,55μ = 0,00

15. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Standard Deviation & Variance
15
The average distance from the mean.
(Gravetter & Wallnau, 2012: 113)
FOR POPULATION
find the deviation
(distance from the mean)
for each score
square each deviation
find the average
of the squared deviations
take the square root
of the variance
STANDARD
DEVIATION
VARIANCE

16. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Standard Deviation & Variance
16
The average distance from the mean.
(Gravetter & Wallnau, 2012: 114)
FOR SAMPLES
11 14 13 13 14 14 23 13 15 14
8 15 17 15 14 15 16 16 14 13
11 16 13 15 16
POPULATION
SAMPLES

17. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Standard Deviation & Variance
17
The average distance from the mean.
(Gravetter & Wallnau, 2012: 114)
FOR SAMPLES
X X - M (X - M)2
11 -3,20 10,24
13 -1,20 1,44
15 0,80 0,64
16 1,80 3,24
16 1,80 3,24
find the deviation
(distance from the mean)
for each score
square each deviation
find the average
of the squared deviations
take the square root
of the variance
3,76
1,96
M = 14,20 SS = 18,80M = 0,00

18. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Standard Deviation & Variance
18
The average distance from the mean.
(Gravetter & Wallnau, 2012: 114)
FOR SAMPLES
11 14 13 13 14 14 23 13 15 14
8 15 17 15 14 15 16 16 14 13
11 16 13 15 16
POPULATION
SAMPLES
lessvariability
POPULATION
VARIABILITY
SAMPLES
VARIABILITY
biasedestimate

19. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Standard Deviation & Variance
19
The average distance from the mean.
(Gravetter & Wallnau, 2012: 117-118)
FOR SAMPLES
μ = 14,35
?
M ≈ 14,35
n = 5
11
16
13
15
No restrictions
Restricted
DEGREES OF
FREEDOM

20. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Standard Deviation & Variance
20
The average distance from the mean.
(Gravetter & Wallnau, 2012: 114)
FOR SAMPLES
X X - M (X - M)2
11 -3,20 10,24
13 -1,20 1,44
15 0,80 0,64
16 1,80 3,24
16 1,80 3,24
find the deviation
(distance from the mean)
for each score
square each deviation
find the average
of the squared deviations
take the square root
of the variance
STANDARD
DEVIATION
VARIANCE 4,70
2,17
M = 14,20 SS = 18,80M = 0,00

21. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Standard Deviation & Variance
21
The average distance from the mean.
(Gravetter & Wallnau, 2012: 117-118)
find the deviation
(distance from the mean)
for each score
square each deviation
find the average
of the squared deviations
take the square root
of the variance
STANDARD
DEVIATION
VARIANCE
FOR SAMPLES

22. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Standard Deviation & Variance
22
The average distance from the mean.
TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS
COUNT vs MEASURE ☐ COUNT ☐ MEASURE
MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO
ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH
✓
✓ ✓
✓
✓

23. Selecting a Measure

24. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Selecting a Measure
24
OF CENTRAL TENDENCY & VARIABILITY
TYPE OF VARIABLES
MEASUREMENT SCALE
CENTRAL TENDENCY THE MODE
THE
MEDIAN
THE
MEAN
VARIABILITY
COUNT OF
VARIATIONS
THE
RANGE
THE
INTERQUARTILE
RANGE
STANDARD
DEVIATION
VARIANCE
DISCRETE
CONTINUOUS
NOMINAL
ORDINAL
INTERVAL
RATIO

25. PDU 207 STATISTIK DASAR 2016 © Ardhiati 25
WANT TO KNOW MORE?
Gravetter, F.J. & Wallnau, L.B. (2012).
Statistics for the behavioral sciences (9th ed.).
Australia: WADSWORTH CENGAGE Learning.