This document provides an overview of central tendency techniques in statistics. It defines central tendency as a statistical measure to find the most typical or representative score of a distribution. The document discusses the three main measures of central tendency: the mean, median, and mode. It explains how to calculate and interpret each measure and when each is the most appropriate technique to use depending on the type of data and goals of analysis. The document also discusses how the shape of a distribution, whether symmetrical or skewed, impacts which central tendency measure best describes the center of the data.

1. PDU 207 STATISTIK DASAR
SEKSI E
SEMESTER GASAL 2016/2017
FAKULTAS PSIKOLOGI / PROGRAM STUDI S1 PSIKOLOGI
Central Tendency
KULIAH IV – 29 AGUSTUS 2016

2. Menguasai teknik-teknik statistika deskriptif dan statistika inferensial,
secara khusus terkait dengan:
• Tujuan dilakukannya perhitungan central tendency;
• Definisi dan perhitungan tiap teknik pengukuran central tendency.
Memiliki kemampuan menyampaikan argumentasi dan penalaran
dengan bahasa yang tepat, khususnya berkaitan dengan:
• Pemilihan teknik perhitungan central tendency yang paling tepat sesuai jenis data
dan tujuan pengukuran.
One-Day Objectives

3. Introduction to
Central Tendency

4. PDU 207 STATISTIK DASAR 2016 © Ardhiati 4
• Independent Variable:
Instructor
• Dependent Variable:
Short-Term Memory
Capacity
5 4 3 3
4 4 7 5
2 5 4 3
4 8 3 5
5 6 6 4
8 6 6 5
7 8 8 7
8 9 7 8
7 9 5 8
7 7 6 7
GROUP 1 GROUP 2
IMAGE SOURCES: unitedgiveaways.com/tag/scarlett-johansson/ ;
fansshare.com/gallery/photos/12369098/julia-bperez-bcopy/

5. PDU 207 STATISTIK DASAR 2016 © Ardhiati 5
• Independent Variable:
Instructor
• Dependent Variable:
Short-Term Memory
Capacity
GROUP 1 GROUP 2
IMAGE SOURCES: unitedgiveaways.com/tag/scarlett-johansson/ ;
fansshare.com/gallery/photos/12369098/julia-bperez-bcopy/
0
1
3
4
6
7
9
10
1 2 3 4 5 6 7 8 9 10
Group 1 Group 2
How far these
two groups differ?
CENTRAL
TENDENCY

6. PDU 207 STATISTIK DASAR 2016 © Ardhiati 6
The general purpose of
descriptive statistical methods
is to summarize, organize, and simplify data;
Organize or summarize them
in a form that is more manageable.
(Gravetter & Wallnau, 2012: 72)
CENTRAL
TENDENCY

7. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Central Tendency
7
Central tendency is a statistical measure
to determine a single score that defines
the center of a distribution.
The goal of central tendency is to find
the single score that is most typical or
most representative of the entire group.
THE DEFINITION
(Gravetter & Wallnau, 2012: 73)

8. PDU 207 STATISTIK DASAR 2016 © Ardhiati 8
CENTRAL
TENDENCY
THE
MEAN
THE
MEDIAN
THE
MODE

9. The Mean,
Median, & Mode

10. PDU 207 STATISTIK DASAR 2016 © Ardhiati
The Mean
10
• the sum of the scores divided by the number of scores;
• the amount each individual receives when the total (∑X) is
divided equally among all of the individuals (N) in the distribution;
• a balance point for the distribution.
FOR A DISTRIBUTION IS…
(Gravetter & Wallnau, 2012: 74-77)

11. PDU 207 STATISTIK DASAR 2016 © Ardhiati
The Mean
11
• Changing a score
Changing the value of any score changes the mean;
• Introducing a new score or
removing a score
Adding a new score to a distribution, or removing
an existing score, usually changes the mean;
ALTERNATIVE DEFINITION
(Gravetter & Wallnau, 2012: 79-82)
• Adding or subtracting a constant
from each score
If a constant value is added to every score in a
distribution, the same constant is added to the mean;
• Multiplying or dividing each score
by a constant
If every score in a distribution is multiplied by
(or divided by) a constant value, the mean changes
in the same way.

12. PDU 207 STATISTIK DASAR 2016 © Ardhiati
The Median
12
• the midpoint of the list if the scores in a distribution are listed in order
from smallest to largest;
• the point on the measurement scale below which 50% of the scores in the
distribution are located.
FOR A DISTRIBUTION IS…
(Gravetter & Wallnau, 2012: 83-85)

13. PDU 207 STATISTIK DASAR 2016 © Ardhiati
The Mode
13
• the score or category that has the greatest frequency.
FOR A DISTRIBUTION IS…
(Gravetter & Wallnau, 2012: 87-89)

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Locate
the “center”
of the distribution! 1 2 3 4 5 6 7 8 9
f
X
1 2 3 4 5 6 7 8 9
f
X1 2 3 4 5 6 7 8 9
f
X
(Gravetter & Wallnau, 2012: 74)

15. PDU 207 STATISTIK DASAR 2016 © Ardhiati 15
There are other things need to be considered
before analyzing the central tendency
of the data.
Not all techniques
are appropriate for all kind of data.
SO…

16. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Selecting a Measure
16
OF CENTRAL TENDENCY
The Mean The Median The Mode
Ratio/Interval Scale
Undetermined Values
Ordinal Scale
Nominal Scale
Discrete Variables
Describing Shape
Open-Ended Distribution
✓
Extreme Scores/Skewed Distributions
✓
✓
✓
✓
✓
✓
✓
(Gravetter & Wallnau, 2012: 89-92)

17. Central Tendency &
The Shape of Distribution

18. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Central Tendency
18
IN A SYMMETRICAL DISTRIBUTION
The mean and median are close together
in the center of the distribution.
& THE SHAPE OF DISTRIBUTION
(Gravetter & Wallnau, 2012: 95-96)

19. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Central Tendency
19
IN A SKEWED DISTRIBUTION
& THE SHAPE OF DISTRIBUTION
(Gravetter & Wallnau, 2012: 95-96)

20. PDU 207 STATISTIK DASAR 2016 © Ardhiati 20
WANT TO KNOW MORE?
Gravetter, F.J. & Wallnau, L.B. (2012).
Statistics for the behavioral sciences (9th ed.).
Australia: WADSWORTH CENGAGE Learning.