statistika dasar (4) variasi data

UNIVERSITAS NEGERI JAKARTA

Pertemuan 4UKURAN PEMUSATAN DAN LOKASI

Hdi Nasbey, M.SiJurusan FisikaFakultas Matematika dan Ilmu Pemgetahuan Alam

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Outline

Penyajian Data Beberapa contoh daftar statistic Diagram Batang Diagram garis Diagram lingkaran dan diagram pastel Diagram lambing Diagram peta Diagram Pencar

12/04/23 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 2

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Learning Outcomes

Pada akhir pertemuan ini, diharapkan mahasiswa

akan mampu : Mahasiswa akan dapat menghitung ukuran-

ukuran pemusatan dan lokasi.

12/04/23© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

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Outline Materi

Rata-rata Median Modus Kuartil Desil persentil


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Measures of Center

A measure along the horizontal axis of the data distribution that locates the center center of the distribution.


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1. Arithmetic Mean or Average

The mean mean of a set of measurements is the sum of the measurements divided by the total number of measurements.

n

xx i

n

xx i

where n = number of measurementstsmeasuremen the all of sum ix


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Example

•The set: 2, 9, 1, 5, 6

n

xx i 6.6

5

33

5

651192

If we were able to enumerate the whole population, the population meanpopulation mean would be called (the Greek letter “mu”).


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Mean (Arithmetic Mean)

Approximating the Arithmetic Mean• Used when raw data are not available

• 1

sample size

number of classes in the frequency distribution

midpoint of the th class

frequencies of the th class

c

j jj

j

j

m f

Xn

n

c

m j

f j


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2. Median

• The median median of a set of measurements is the middle measurement when the measurements are ranked from smallest to largest.

• The position of the medianposition of the median is

.5(.5(nn + 1) + 1)

once the measurements have been ordered.

a. Md = X(n+1)/2 12/04/23

© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

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Example

The set: 2, 4, 9, 8, 6, 5, 3 n = 7 Sort: 2, 3, 4, 5, 6, 8, 9 Position: .5(n + 1) = .5(7 + 1) = 4th

Median = 4th largest measurement

• The set: 2, 4, 9, 8, 6, 5 n = 6

• Sort:2, 4, 5, 6, 8, 9

• Position: .5(n + 1) = .5(6 + 1) = 3.5th Median = (5 + 6)/2 = 5.5 — average of the 3rd and 4th measurements


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b. Median Data Berkelompok

f

FnpbMe 2

1


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3. ModeUntuk menyatakan fenomena yang paling

banyak terjadi, juga untuk menentukan “rata-rata” dari data kualitatif.

a. Data tak berkelompok : Modus (Mo) dilihat dari data yang memiliki frekuensi terbanyak

The set: 2, 4, 9, 8, 8, 5, 3• The mode is 88, which occurs twice

The set: 2, 2, 9, 8, 8, 5, 3• There are two modes—88 and 22 (bimodalbimodal)

The set: 2, 4, 9, 8, 5, 3• There is no modeno mode (each value is unique).


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b. Modus Data Berkelompok

3,2,1;4

)1(

i

niXQi

4. Kuartil (Qi)Membagi kelompok data yang telah terurut menjadi 4 bagian yang sama besar.

a. Data tak berkelompok

4. Kuartil (Qi)Membagi kelompok data yang telah terurut menjadi 4 bagian yang sama besar.

a. Data tak berkelompok

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1

bb

bpbMo


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b. Kuartil Data Berkelompok

3,2,1;4

i

f

Fni

pbQi


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Example

Mean?

Median?

Mode? (Highest peak)

The number of quarts of milk purchased by 25 households:

0 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 5

2.225

55

n

xx i

2m

2mode


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Extreme Values The mean is more easily affected by extremely

large or small values than the median.

AppletApplet

•The median is often used as a measure of center when the distribution is skewed.


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Extreme Values

Skewed left: Mean < Median

Skewed right: Mean > Median

Symmetric: Mean = Median


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5. Desil Membagi kelompok data yang telah terurut

menjadi 10 bagian yang sama besar.a. Data tak berkelompok

b. Data berkelompok

9...,,2,1;10

)1( iXD nii

9,...,2,1;10

i

f

Fni

pbDi


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6. Persentil (Pi) Membagi kelompok data yang telah terurut

menjadi 100 bagian yang sama besar.a. Data tak berkelompok

b. Data berkelompok

9...,,2,1;10

)1( iXP nii

9,...,2,1;100

i

f

Fni

pbPi


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Selamat Belajar Semoga Sukses.


statistika dasar (4) variasi data

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