Ee184405 statistika dan stokastik statistik deskriptif 1 grafik

DepartemenTeknik Elektro
FakultasTeknologi Elektro dan Informatika Cerdas
InstitutTeknologi Sepuluh Nopember
Bab 3
Statistik Deskriptif 1:
Representasi Grafik
EE184405 Probabilitas, Statistika, & Proses Stokastik

Pengantar
CP Pengetahuan
• Menguasai konsep statistik deskriptif data dengan teknik grafis: histogram, pie
chart dan teknik numerik berupa lokasi, sebaran, dan variabilitas data.
CP Keterampilan
• Mampu merepresentasikan data dalam bentuk grafis secara manual
maupun menggunakan alat bantu software R.
• Mampu merepresentasikan data dalam bentuk numerik serta menentukan
lokasi, sebaran dan variabilitas data melalui perhitungan manual maupun
menggunakan alat bantu software R.
Pengantar Fakta Konsep Ringkasan Latihan Asesmen

Pengantar
Statistika adalah suatu bidang ilmu yang mempelajari cara-cara
mengumpulkan data untuk selanjutnya dapat dideskripsikan dan diolah,
kemudian melakukan induksi/inferensi dalam rangka membuat
kesimpulan, agar dapat ditentukan keputusan yang akan diambil
berdasarkan data yang dimiliki.
DATA =============> PROSES STATISTIK ===========> INFORMASI
Statistik Deskriptif adalah suatu cara menggambarkan persoalan yang
berdasarkan data yang dimiliki yakni dengan cara menata data tersebut
sedemikian rupa agar karakteristik data dapat dipahami dengan mudah
sehingga berguna untuk keperluan selanjutnya.

Fakta
Sebagai contoh, suatu perusahaan Pabrik Elektronik ingin mengetahui
secara pasti perkembangan marketing produknya dipasaran local, maka
dilakukan aktivitas pengumpulan data time series untuk jangka waktu
tertentu (periodik), dan di lakukan deskripsi melalui analisis tren.
Contoh yang lain, seorang MahasiswaTeknik Elektro ingin meneliti berapa
rata-rata kuota data yang dibutuhkan per sks perkuliahan online dalam
beberapa mode, misal: mode sinkron menggunakan aplikasi telekonferensi
dan mode asinkron dengan menyediakan video lecture pada platform e-
learning. Maka dilakukan survai pengumpulan data pada pelaksanaan
beberapa perkuliahan yang mewakili mode sinkron dan mode asinkron,
untuk pengamatan periode tertentu, dan dihitung rata-ratanya melalui
olahan data sampel pengamatan tadi.

Konsep: Categorical Data
Categorical
Tabulating
Data
Graphing
Data
Bar Charts Pie Charts
Pareto
Diagram

© 2002 Prentice-Hall, Inc.
Chap 2-6
Graphing Categorical Data: Univariate Data
Categorical Data
Tabulating Data
The Summary Table
0 1 0 2 0 3 0 4 0 5 0
S t o c k s
B o n d s
S a vin g s
C D
Graphing Data
Pie Charts
Pareto DiagramBar Charts
0
5
1 0
1 5
2 0
2 5
3 0
3 5
4 0
4 5
S t o c k s B o n d s S a vin g s C D
0
2 0
4 0
6 0
8 0
1 0 0
1 2 0

Categorical Data: SummaryTable (for an Political Parties)
Investment Category Total Percentage
(in thousands) (in %)
Republics 46.5 42.27
Labors 32 29.09
Democrats 15.5 14.09
Teachers 16 14.55
Total 110 100
Variables are Categorical

Bivariate Categorical Data
Political Parties Perth Sydney Canberra Total Category
Republics 46.5 55 27.5 129
Labors 32 44 19 95
Democrats 15.5 20 13.5 49
Teachers 16 28 7 51
Total 110 147 67 324
• Contingency tables: choosers in thousands

Chap 2-9
Bar Chart (for Political Parties)
0 10 20 30 40 50
Republics
Labors
Democrats
Teachers
Amount in thousands
Political Parties

Chap 2-10
Pie Chart (for Political Parties)
Percentages are
rounded to the
nearest percent.
Amount in Thousands
Teachers
15%
Democrats
14%
Labors
29%
Republics
42%

Chap 2-11
Pareto Diagram
Axis for line
graph
shows
cumulative
% chosen
Axis for
bar
chart
shows
%
chosen
in each
category
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
Stocks Bonds Savings CD
Republics Labors Teachers Democrats

Chap 2-12
Tabulating & Graphing Bivariate Categorical Data
• Side by side charts
0 10 20 30 40 50 60
Republics
Labors
Teachers
Democrats
Comparing Investors
Canberra Sydney Perth

Chap 2-13
Principles of Graphical Excellence
• Presents data in a way that provides substance, statistics
and design
• Communicates complex ideas with clarity, precision and
efficiency
• Gives the largest number of ideas in the most efficient
manner
• Almost always involves several dimensions
• Tells the truth about the data

Chap 2-14
• Using “chart junk”
• Failing to provide a relative basis in comparing data between groups
• Compressing the vertical axis
• Providing no zero point on the vertical axis
Errors in Presenting Data

Chap 2-15
“Chart Junk”
Good Presentation
1960: $1.00
1970: $1.60
1980: $3.10
1990: $3.80
Minimum Wage Minimum Wage
0
2
4
1960 1970 1980 1990
$
Bad Presentation 

Chap 2-16
No Relative Basis
Good Presentation
A’s received by
students.
A’s received by
students.
Bad Presentation
0

200
300
FR SO JR SR
Freq.

10

30
FR SO JR SR
%
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior


Chap 2-17
CompressingVertical Axis
Good Presentation
Quarterly Sales Quarterly Sales
Bad Presentation
0
25
50
Q1 Q2 Q3 Q4
$
0
100
200
Q1 Q2 Q3 Q4
$


Chap 2-18
No Zero Point onVertical Axis
Good Presentation
Monthly Sales
Monthly Sales
Bad Presentation
0
39
42
45
J F M A M J
$
36
39
42
45
J F M A M J
$
Graphing the first six months of sales.
36


Chap 2-19
Tabulating and Graphing Numerical Data
0
1
2
3
4
5
6
7
1 0 2 0 3 0 4 0 5 0 6 0
Numerical Data
Ordered Array
Stem and Leaf
Display
Histograms Ogive
Tables
2 144677
3 028
4 1
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Frequency Distributions
Cumulative Distributions
Polygons
O give
0
2 0
4 0
6 0
8 0
1 0 0
1 2 0
1 0 2 0 3 0 4 0 5 0 6 0

Frequency Distributions, Relative Frequency Distributions and
Percentage Distributions
© 2002 Prentice-Hall, Inc. Chap
2-20
Class Frequency
10 but under 20 3 .15 15
20 but under 30 6 .30 30
30 but under 40 5 .25 25
40 but under 50 4 .20 20
50 but under 60 2 .10 10
Total 20 1 100
Relative
Frequency Percentage
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Chap 2-21
Graphing Numerical Data:The Histogram
Histogram
0
3
6
5
4
2
0
0
1
2
3
4
5
6
7
5 15 25 36 45 55 More
Frequency
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
No Gaps
Between
Bars
Class Midpoints
Class Boundaries

Chap 2-22
Graphing Numerical Data:The Frequency Polygon
F r e q u e n c y
0
1
2
3
4
5
6
7
5 1 5 2 5 3 6 4 5 5 5 M o r e
Class Midpoints
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Chap 2-23
Tabulating Numerical Data: Cumulative Frequency
Cumulative Cumulative
Class Frequency % Frequency
10 but under 20 3 15
20 but under 30 9 45
30 but under 40 14 70
40 but under 50 18 90
50 but under 60 20 100
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Chap 2-24
Graphing Numerical Data:The Ogive (Cumulative % Polygon)
Ogive
0
20
40
60
80
100
10 20 30 40 50 60
Class Boundaries (Not Midpoints)
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Chap 2-25
• Data in raw form (as collected):
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
• Data in ordered array from smallest to largest:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
• Stem-and-leaf display:
Organizing Numerical Data
2 144677
3 028
4 1

Chap 2-26
Graphing Bivariate Numerical Data (Scatter Plot)
Mutual Funds Scatter Plot
0
10
20
30
40
0 10 20 30 40
Net Asset Values
TotalYearto
DateReturn
(%)

Variables and Data
• A variable is a characteristic that changes or varies over time and/or for
different individuals or objects under consideration.
• Examples: Hair color, white blood cell count, time to failure of a
computer component.

Definitions
• An experimental unit is the individual or object on which a variable is
measured.
• A measurement results when a variable is actually measured on an
experimental unit.
• A set of measurements, called data, can be either a sample or a
population.

Example
•Variable
•Hair color
•Experimental unit
•Person
•Typical Measurements
•Brown, black, blonde, etc.

Example
•Variable
•Time until a
light bulb burns out
•Experimental unit
•Light bulb
•Typical Measurements
•1500 hours, 1535.5 hours, etc.

How many variables have you measured?
•Univariate data: One variable is measured on a
single experimental unit.
•Bivariate data: Two variables are measured on a
single experimental unit.
•Multivariate data: More than two variables are
measured on a single experimental unit.

Types ofVariables
Qualitative
Discrete Continuous
Quantitative

Types ofVariables
•Qualitative variables measure a quality or
characteristic on each experimental unit.
•Examples:
•Hair color (black, brown, blonde…)
•Make of car (Dodge, Honda, Ford…)
•Gender (male, female)
•State of birth (California, Arizona,….)

Types ofVariables
•Quantitative variables measure a
numerical quantity on each
experimental unit.
Discrete if it can assume only a finite
or countable number of values.
Continuous if it can assume the
infinitely many values corresponding to
the points on a line interval.

Examples
•For each orange tree in a grove, the number of
oranges is measured.
•Quantitative discrete
•For a particular day, the number of cars entering a
college campus is measured.
•Quantitative discrete
•Time until a light bulb burns out
•Quantitative continuous

Graphing QualitativeVariables
•Use a data distribution to describe:
•What values of the variable have been measured
•How often each value has occurred
•“How often” can be measured 3 ways:
•Frequency
•Relative frequency = Frequency/n
•Percent = 100 x Relative frequency

Example
• A bag of M&Ms contains 25 candies:
•Raw Data:
•StatisticalTable:
Color Tally Frequency Relative
Frequency
Percent
Red 3 3/25 = .12 12%
Blue 6 6/25 = .24 24%
Green 4 4/25 = .16 16%
Orange 5 5/25 = .20 20%
Brown 3 3/25 = .12 12%
Yellow 4 4/25 = .16 16%
m
m
mm
m
m
m m
m
m
mm m
m
m
mm
m
m
m
m
m
m
mmm
mm
m
m m
m m
m m m
m m m
m m
m m
mm
m
m
m m
m

Graphs
Bar Chart
Pie Chart
Color
Frequency
GreenOrangeBlueRedYellowBrown
6
5
4
3
2
1
0
16.0%
Green
20.0%
Orange
24.0%
Blue
12.0%
Red
16.0%
Yellow
12.0%
Brown

Graphing QuantitativeVariables
• A single quantitative variable measured for different
population segments or for different categories of
classification can be graphed using a pie or bar chart.
A Big Mac
hamburger costs
$4.90 in Switzerland,
$2.90 in the U.S. and
$1.86 in South
Africa.
Country
CostofaBigMac($)
South AfricaU.S.Switzerland
5
4
3
2
1
0

• A single quantitative variable measured over
time is called a time series. It can be graphed
using a line or bar chart.
Sept Oct Nov Dec Jan Feb Mar
178.10 177.60 177.50 177.30 177.60 178.00 178.60
CPI: All Urban Consumers-Seasonally Adjusted

Dotplots
•The simplest graph for quantitative data
•Plots the measurements as points on a horizontal axis,
stacking the points that duplicate existing points.
•Example: The set 4, 5, 5, 7, 6
4 5 6 7

Stem and Leaf Plots
•A simple graph for quantitative data
•Uses the actual numerical values of each data point.
–Divide each measurement into two parts: the stem
and the leaf.
–List the stems in a column, with a vertical line to their
right.
–For each measurement, record the leaf portion in the
same row as its matching stem.
–Order the leaves from lowest to highest in each stem.
–Provide a key to your coding.

Example
The prices ($) of 18 brands of walking shoes:
90 70 70 70 75 70 65 68 60
74 70 95 75 70 68 65 40 65
4 0
5
6 5 8 0 8 5 5
7 0 0 0 5 0 4 0 5 0
8
9 0 5
4 0
5
6 0 5 5 5 8 8
7 0 0 0 0 0 0 4 5 5
8
9 0 5
Reorder

Interpreting Graphs: Location and Spread
•Where is the data centered on the horizontal axis, and
how does it spread out from the center?

Interpreting Graphs: Shapes
Mound shaped and symmetric
(mirror images)
Skewed right: a few unusually
large measurements
Skewed left: a few unusually
small measurements
Bimodal: two local peaks

Interpreting Graphs: Outliers
• Are there any strange or unusual measurements that stand out in the
data set?
OutlierNo Outliers

Example
• A quality control process measures the diameter of a gear
being made by a machine (cm).The technician records 15
diameters, but inadvertently makes a typing mistake on the
second entry.
1.991 1.891 1.991 1.988 1.993 1.989 1.990 1.988
1.988 1.993 1.991 1.989 1.989 1.993 1.990 1.994

Relative Frequency Histograms
•A relative frequency histogram for a quantitative
data set is a bar graph in which the height of the bar
shows “how often” (measured as a proportion or
relative frequency) measurements fall in a particular
class or subinterval.
Create
intervals
Stack and draw bars

• Divide the range of the data into 5-12 subintervals of
equal length.
• Calculate the approximate width of the subinterval as
Range/number of subintervals.
• Round the approximate width up to a convenient value.
• Use the method of left inclusion, including the left
endpoint, but not the right in your tally.
• Create a statistical table including the subintervals, their
frequencies and relative frequencies.

• Draw the relative frequency histogram, plotting the subintervals on the
horizontal axis and the relative frequencies on the vertical axis.
• The height of the bar represents
•The proportion of measurements falling in that
class or subinterval.
•The probability that a single measurement, drawn
at random from the set, will belong to that class or
subinterval.

Example
The ages of 50 tenured faculty at a state university.
34 48 70 63 52 52 35 50 37 43 53 43 52 44
42 31 36 48 43 26 58 62 49 34 48 53 39 45
34 59 34 66 40 59 36 41 35 36 62 34 38 28
43 50 30 43 32 44 58 53
• We choose to use 6 intervals.
• Minimum class width = (70 – 26)/6 = 7.33
• Convenient class width = 8
• Use 6 classes of length 8, starting at 25.

Age Tally Frequency Relative
Frequency
Percent
25 to < 33 1111 5 5/50 = .10 10%
33 to < 41 1111 1111 1111 14 14/50 = .28 28%
41 to < 49 1111 1111 111 13 13/50 = .26 26%
49 to < 57 1111 1111 9 9/50 = .18 18%
57 to < 65 1111 11 7 7/50 = .14 14%
65 to < 73 11 2 2/50 = .04 4%
Ages
Relativefrequency
73655749413325
14/50
12/50
10/50
8/50
6/50
4/50
2/50
0

Shape?
Outliers?
What proportion of the
tenured faculty are
younger than 41?
What is the probability that
a randomly selected
faculty member is 49 or
older?
Skewed right
No.
(14 + 5)/50
= 19/50 = .38
(8 + 7 + 2)/50 = 17/50 = .34
Ages
Relativefrequency
73655749413325
14/50
12/50
10/50
8/50
6/50
4/50
2/50
0
Describing the Distribution

Key Concepts (1/2)
I. How Data Are Generated
1. Experimental units, variables, measurements
2. Samples and populations
3. Univariate, bivariate, and multivariate data
II.Types ofVariables
1. Qualitative or categorical
2. Quantitative
a. Discrete
b. Continuous
III. Graphs for Univariate Data Distributions
1. Qualitative or categorical data
a. Pie charts
b. Bar charts

Key Concepts (2/2)
2. Quantitative data
a. Pie and bar charts
b. Line charts
c. Dotplots
d. Stem and leaf plots
e. Relative frequency histograms
3. Describing data distributions
a. Shapes—symmetric, skewed left, skewed right,
unimodal, bimodal
b. Proportion of measurements in certain intervals
c. Outliers

Latihan 1

Latihan 2

Latihan 3
• Seribu warga Minnesota dimintai pendapat tentang
musim yang paling mereka sukai. Hasilnya adalah
100 orang menyukai musim dingin, 300 orang
penyuka musim semi, 400 orang menyukai musim
panas dan 200 orang menyukai musim gugur.
• Dalam membuat tabel frekuensi, berapa kelas yang
harus dibuat untuk data tersebut?
• Bagaimana frekuensi relatif untuk tiap kelas?

Latihan 4
• Wellstone Inc., ingin membuat dan memasarkan rangka
ponsel dalam 5 warna: putih, hitam, hijau, oranye dan merah.
Sebelum melakukan produksi masal, perusahaan tersebut
membuka gerai mall dan mendapatkan hasil dari survey
singkat sbb:
Putih 130
Hitam 104
Kuning 325
Hijau 455
Merah 286
• Disebut apa tabel disamping?
• Buatlah diagram batangnya
• Buatlah diagram pienya.
• JikaWellstone Inc. berencana
memproduksi 1 juta ponsel, berapa rangka
dari tiap warna harus diproduksi?

Latihan 5
• Quick Change Oil Company memiliki sejumlah gerai
di kota Seattle. Jumlah pelanggan yang mengganti
oli di gerai mereka selama 36 hari terakhir. Buatlah
histogramnya.
65 98 55 62 79 59 51 90 72
56 70 62 66 80 94 79 63 73
71 85 77 18 63 84 38 54 50
59 54 56 36 26 50 34 44 41

Praktikum dan Kuis Online
•Percobaan 1
• Representasi Data
•Kuis Online: Senin, 20 April 2020 (tentative)

Ee184405 statistika dan stokastik statistik deskriptif 1 grafik

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