Matakuliah
Tahun
Versi
: I0134 – Metoda Statistika
: 2005
: Revisi
Pertemuan 02
Statistika Deskriptif
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa dapat memberikan definisi
istilah statistika, pengumpulan data dan
pengukuran.
• Mahasiswa dapat menjelaskan metode
pengumpulan, pengolahan dan penyajian
data.
2
Outline Materi
•
•
•
•
Peranan Statistika dan statistik
Diagram dahan dan daun
Diagram kotak garis
Data pencilan
3
Statistika Deskriptif
Sales Sorted Sales
9
6
12
10
13
15
16
14
14
16
17
16
24
21
22
18
19
18
20
17
6
9
10
12
13
14
14
15
16
16
16
17
17
18
18
19
20
21
22
24
4
Example Percentiles





Find the 50th, 80th, and the 90th percentiles of this
data set.
To find the 50th percentile, determine the data point
in position (n + 1)P/100 = (20 + 1)(50/100) = 10.5.
Thus, the percentile is located at the 10.5th position.
The 10th observation is 16, and the 11th observation is
also 16.
The 50th percentile will lie halfway between the 10th
and 11th values and is thus 16.
5
Example Percentiles




To find the 80th percentile, determine the data point
in position (n + 1)P/100 = (20 + 1)(80/100) = 16.8.
Thus, the percentile is located at the 16.8th position.
The 16th observation is 19, and the 17th observation
is also 20.
The 80th percentile is a point lying 0.8 of the way
from 19 to 20 and is thus 19.8.
6
Example Percentiles




To find the 90th percentile, determine the data point
in position (n + 1)P/100 = (20 + 1)(90/100) = 18.9.
Thus, the percentile is located at the 18.9th position.
The 18th observation is 21, and the 19th observation
is also 22.
The 90th percentile is a point lying 0.9 of the way
from 21 to 22 and is thus 21.9.
7
Quartiles




Quartiles are the percentage points that break down
the data set into quarters.
The first quartile is the 25th percentile. It is the point
below which lie 1/4 of the data.
The second quartile is the 50th percentile. It is the
point below which lie 1/2 of the data. This is also
called the median.
The third quartile is the 75th percentile. It is the
point below which lie 3/4 of the data.
8
Quartiles and Interquartile
Range




The first quartile (25th percentile) is
often called the lower quartile.
The second quartile (50th percentile) is
often called median or the middle
quartile.
The third quartile (75th percentile) is
often called the upper quartile.
The interquartile range is the difference
between the first and the third quartiles.
9
Example Quartiles
(n+1)P/100
Sales
9
6
12
10
13
15
16
14
14
16
17
16
24
21
22
18
19
18
20
17
Sorted
Sales
6
9
10
12
13
14
14
15
16
16
16
17
17
18
18
19
20
21
22
24
Quartiles
(20+1)25/100=5.25
13 + (.25)(1) = 13.25
Median
(20+1)50/100=10.5
16 + (.5)(0) = 16
Third Quartile
(20+1)75/100=15.75
18+ (.75)(1) = 18.75
First Quartile
10
Summary Measures Population
Parameters Sample Statistics

Measures of Central
Tendency
– Median
– Mode
– Mean

Other summary
measures:
– Skewness
– Kurtosis

Measures of Variability
–
–
–
–
Range
Interquartile range
Variance
Standard Deviation
11
Statistika Deskriptif
Techniques to determine relationships and trends,
identify outliers and influential observations, and
quickly describe or summarize data sets.

Stem-and-Leaf Displays
– Quick-and-dirty listing of all observations
– Conveys some of the same information as a
histogram

Box Plots
– Median
– Lower and upper quartiles
– Maximum and minimum
12
Stem-and-Leaf Display
MTB> Stem-and-Leaf of C1
Stem-and-leaf of C1
Leaf Unit = 1.0
Median is in this class
4
9
18
(7)
17
13
11
8
6
3
2
N = 42
1 1223
1 55567
2 011122234
2 6777899
3 0124
3 57
4 112
4 57
5 023
56
6 02
13
Box Plot
Elements of a Box Plot
Outlier
o
Outer
Fence
Smallest data
point not below
inner fence
Largest data point
Suspected
not exceeding
outlier
inner fence
X
Inner
Fence
Q1-1.5(IQR)
Q1-3(IQR)
X
Q1
Median
Interquartile Range
Q3
Inner
Fence
Q3+1.5(IQR)
*
Outer
Fence
Q3+3(IQR)
14
Box Plot
MTB > BoxPlot c1.
Character Boxplot
------------------------------I +
I------------------------------------------+---------+---------+---------+---------+---------+----C1
10
20
30
40
50
60
MTB >
15
Minitab Descriptive Statistics
Output
Descriptive Statistics
Variable
No_Sales
N
Mean
20 15.850
Median
16.000
Variable
No_Sales
Minimum
6.000
Maximum
24.000
TrMean
15.944
Q1
13.250
StDev
4.464
SE Mean
0.998
Q3
18.750
MTB >
16
Excel Descriptive Statistics
Output
Column1
Mean
15.85
Standard Error
0.99809
Median
16
Mode
16
Standard Deviation 4.463595
Sample Variance
19.92368
Kurtosis
0.115608
Skewness
-0.35153
Range
18
Minimum
6
Maximum
24
Sum
317
Count
20
17
• Selamat Belajar Semoga Sukses
18