Question

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2) A semiconductor manufacturer produces printed circuit boards that are sampled to determine the thickness of their copper plating. The following statements create a data set named Trans, which contains the plating thicknesses (Thick) of 50 boards:

3.412

3.45

3.551

3.451

3.60

3.462

3.586

3.645

3.252

3.62

3.606

3.634

3.852

3.56

3.342

3.341

3.444

3.774

3.632

3.199

3.71

3.654

3.723

3.981

3.934

3.708

3.934

3.315

3.762

3.223

3.469

3.481

3.515

3.535

3.46

3.575

3.488

3.515

3.484

3.482

3.517

3.483

3.467

3.467

3.502

3.471

3.516

3.474

3.5

3.466

a. Using /R find the mean, median, mode, range, variance and standard deviation of the data. Attach your output from R.

b. Based on the results in part a, construct the intervals and for the data set. Be sure to show your interval below. What percentage of the measurements for the data set falls in each interval? Compare the intervals , and . Explain why the results are different.

Answer 1

FIRST LET US MAKE VECTOR X OF DATASET.

> x<-c(3.412,3.45,3.551,3.451,3.6,3.462,3.586,3.645,3.252,3.62,3.606,3.634,3.852,3.56,3.342,3.341,3.444,3.774,3.632,3.199,3.71,3.654,3.723,3.981,3.934,3.708,3.934,3.315,3.762,3.223,3.469,3.481,3.515,3.535,3.46,3.575,3.488,3.515,3.484,3.482,3.517,3.483,3.467,3.467,3.502,3.471,3.516,3.474,3.5,3.466)
> x
[1] 3.412 3.450 3.551 3.451 3.600 3.462 3.586 3.645 3.252 3.620 3.606 3.634 3.852 3.560 3.342 3.341 3.444 3.774 3.632 3.199 3.710 3.654 3.723 3.981 3.934 3.708 3.934
[28] 3.315 3.762 3.223 3.469 3.481 3.515 3.535 3.460 3.575 3.488 3.515 3.484 3.482 3.517 3.483 3.467 3.467 3.502 3.471 3.516 3.474 3.500 3.466

MEAN OF DATA
> mean(x)
[1] 3.54448

MEDIAN
> median(x)
[1] 3.5085

RANGE
> range(x)
[1] 3.199 3.981

VARIANCE
> var(x)
[1] 0.02837519

STANDARD DEVIATION
> std<-sqrt(var(x))
> std
[1] 0.1684494