Question

In: Statistics and Probability

A Company manufactures an insulation stripping tool that peels insulation from electric wiring 1/8” to 1/4”...

A Company manufactures an insulation stripping tool that peels insulation from electric wiring 1/8” to 1/4” in diameter. A sample of sixteen tools were randomly selected from the warehouse in order to test the pull-force (in pounds) of the product. The pull-forces of the sixteen tools are shown below:
12.6 12.9 13.4 12.3 13.6 13.5 12.6 13.1 12.5 13.2 13.0 12.5 13.5 12.4 12.2 12.7
Determine: Mean, Median, Qaurtile1, Qaurtile3, Range, S.E.M., Mode, Outlier(s), Variance, Standard Deviation,
Inter-Quartile Range, Max & Min. Note: All calculations must be shown.

Expert Solution

(1)

Mean = 206/16 = 12.875

(2)

Arranging data in ascending order, we get

12.2, 12.3, 12.4, 12.5, 12.5, 12.6, 12.6, 12.7, 12.9, 13.0, 13.1, 13.2, 13.4, 13.5, 13.5, 13.6

n = 16

Median = (16 + 1)/2 th item = average of 8th & 9th items= (12.7 + 12.9)/2 = 12.8

So,

Median = 12.8

(3)

Bottom half is:

12.2, 12.3, 12.4, 12.5, 12.5, 12.6, 12.6, 12.7

The middle of these numbers = 12.5

So,

Quartile1 = Q1 = 12.5

(4)

Upper half is:

12.9, 13.0, 13.1, 13.2, 13.4, 13.5, 13.5, 13.6

Middle of these numbers = 13.3

So,

Quartile 3 = Q3 = 13.3

(5)

Range = Maximum - Minimum = 13.6 - 12.2 = 1.4

(6)

S.E.M.= Standard Error of Mean = Standard Deviation/

= 0.4640/ = 0.116

(7)

Mode = 12.5, 12.6, 13.5

since these 3 values occur 3 times

(8)

IQR = Q3- Q1 = 13.3 - 12.5 = 0.8

Lower = Q1 - 1.5 IQR = 12.5 - (1.5 X 0.8) = 12.5 - 1.2 = 11.3

Upper = Q3 + 1.5 IQR = 13.3 + (1.5 X 0.8) = 13.3 + 1.2 = 14.5

Since all values are within these limits, there are no outliers.

(9)

x	(x-	(x - )²
12.6	- 0.275	0.0756
12.9	0.025	0.0001
13.4	0.525	0.2756
12.3	- 0.575	0.3306
13.6	0.725	0.5256
13.5	0.625	0.3906
12.6	- 0.275	0.0756
13.1	0.225	0.0506
12.5	- 0.375	0.1406
13.2	0.325	0.1056
13.0	0.125	0.0156
12.5	- 0.375	0.1406
13.5	0.625	0.3906
12.4	- 0.475	0.2256
12.2	- 0.675	0.4556
12.7	- 0.175	0.0306
Total =		3.23

Variance = 3.23/15= 0.2153

(10)

Standard deviation =

(11)

Inter-Quartile Range = IQR = Q3- Q1 = 13.3 - 12.5 = 0.8

(12)

Max= 13.6

Min = 12.2

orchestra answered 2 years ago

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