Probabilistik Statistik, Soal 1.2.

Referensi:

Probability & Statistics

for Engineers & Scientists

Ronald E. Walpole

Roanoke College

Raymond H. Myers

Virginia Tech

Sharon L. Myers

Radford University

Keying Ye

University of Texas at San Antonio

Prentice Hall

CONTOH SOAL

1.2 According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 20 pieces of cotton fiber was taken and the absorbency on each piece was measured. The following are the absorbency values:

18.71     21.41     20.72    21.81    19.29     22.43    20.17

23.71    19.44      20.50    18.92    20.33    23.00    22.85

19.25     21.77     22.11    19.77     18.04    21.12

(a) Calculate the sample mean and median for the above sample values.

(b) Compute the 10% trimmed mean.

(c) Do a dot plot of the absorbency data.

(d) Using only the values of the mean, median, and trimmed mean, do you have evidence of outliers in the data?

SOLUSI

a) Mean = (18.71+21.41+20.72+21.81+19.29+22.43+20.17+23.71+19.44+20.50 +18.92+20.33+23.00+22.85+19.25+21.77+22.11 +19.77+18.04+21.12) / 20

Mean = 20.768

Median dari data = 18.04    18.71    18.92    19.25    19.29    19.44    19.77    20.17    20.33    20.50        20.72    20.77     21.12    21.41   21.77    22.11    22.43   22.85  23.00   23.71

Dari data di atas, mediannya adalah (20.50 + 20.72) / 2 –> 20.61

(b) Compute the 10% trimmed mean.

	1	2	3	4	5	6	7	8	9	10
	18,04	18,71	18,92	19,25	19,29	19,44	19,77	20,17	20,33	20,5		20	data
	20,72	21,12	21,41	21,77	21,81	22,11	22,43	22,85	23	23,71		2	ATAS		10,00%
	11	12	13	14	15	16	17	18	19	20		2	BAWAH
1	18,04		JUMLAH									16	SISA DATA
2	18,71		331,89
3	18,92
4	19,25		PEMBAGI
5	19,29		16
6	19,44
7	19,77		the 10% trimmed mean
8	20,17		20,74313
9	20,33
10	20,5
11	20,72
12	21,12
13	21,41
14	21,77
15	21,81
16	22,11
17	22,43
18	22,85
19	23
20	23,71

(c) Do a dot plot of the absorbency data.

(d) Using only the values of the mean, median, and
trimmed mean, do you have evidence of outliers in
the data?

Terdapat perubahan nilai dari data, nilai mean yaitu 20.768 nilai median 20.61, dan nilai trim yang dipangkas 10% yaitu 20,74313

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