The following table contains the measurements of the key length dimension from a
ID: 329358 • Letter: T
Question
The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five were taken at one-hour intervals. Use three-sigma control limits. Use Exhibit 10.13.
OBSERVATIONS
a. Calculate the mean and range for the above samples. (Do not round intermediate calculations. Round your answers to 3 decimal places.)
OBSERVATIONS
SAMPLE NUMBER 1 2 3 4 5 1 0.465 0.494 0.493 0.511 0.472 2 0.471 0.501 0.505 0.484 0.515 3 0.472 0.493 0.516 0.493 0.528 4 0.475 0.501 0.495 0.494 0.492 5 0.481 0.498 0.523 0.457 0.485 6 0.472 0.496 0.502 0.495 0.505 7 0.494 0.502 0.494 0.471 0.504 8 0.505 0.499 0.486 0.472 0.487 9 0.472 0.501 0.507 0.504 0.506 10 0.465 0.502 0.505 0.511 0.485 11 0.495 0.495 0.456 0.494 0.491 12 0.458 0.463 0.525 0.504 0.529 13 0.516 0.502 0.495 0.521 0.504 14 0.491 0.521 0.502 0.495 0.508 15 0.493 0.505 0.487 0.511 0.503 16 0.471 0.501 0.484 0.475 0.525 17 0.481 0.481 0.508 0.473 0.484 18 0.507 0.493 0.495 0.472 0.484 19 0.501 0.539 0.494 0.485 0.493 20 0.513 0.494 0.485 0.504 0.502Explanation / Answer
Calculation is done as follows:
OBSERVATIONS
SAMPLE NUMBER
1
2
3
4
5
Sample Mean
(Average of 5 observation)
Sample
= Range
(Maximum – Minimum)
1
0.465
0.494
0.493
0.511
0.472
0.487
0.046
2
0.471
0.501
0.505
0.484
0.515
0.4952
0.044
3
0.472
0.493
0.516
0.493
0.528
0.5004
0.056
4
0.475
0.501
0.495
0.494
0.492
0.4914
0.026
5
0.481
0.498
0.523
0.457
0.485
0.4888
0.066
6
0.472
0.496
0.502
0.495
0.505
0.494
0.033
7
0.494
0.502
0.494
0.471
0.504
0.493
0.033
8
0.505
0.499
0.486
0.472
0.487
0.4898
0.033
9
0.472
0.501
0.507
0.504
0.506
0.498
0.035
10
0.465
0.502
0.505
0.511
0.485
0.4936
0.046
11
0.495
0.495
0.456
0.494
0.491
0.4862
0.039
12
0.458
0.463
0.525
0.504
0.529
0.4958
0.071
13
0.516
0.502
0.495
0.521
0.504
0.5076
0.026
14
0.491
0.521
0.502
0.495
0.508
0.5034
0.03
15
0.493
0.505
0.487
0.511
0.503
0.4998
0.024
16
0.471
0.501
0.484
0.475
0.525
0.4912
0.054
17
0.481
0.481
0.508
0.473
0.484
0.4854
0.035
18
0.507
0.493
0.495
0.472
0.484
0.4902
0.035
19
0.501
0.539
0.494
0.485
0.493
0.5024
0.054
20
0.513
0.494
0.485
0.504
0.502
0.4996
0.028
Overall Average
(Average of 20 samples)
0.49464
0.0407
Overall Average = 0.4946
Overall Range = 0.0407
OBSERVATIONS
SAMPLE NUMBER
1
2
3
4
5
Sample Mean
(Average of 5 observation)
Sample
= Range
(Maximum – Minimum)
1
0.465
0.494
0.493
0.511
0.472
0.487
0.046
2
0.471
0.501
0.505
0.484
0.515
0.4952
0.044
3
0.472
0.493
0.516
0.493
0.528
0.5004
0.056
4
0.475
0.501
0.495
0.494
0.492
0.4914
0.026
5
0.481
0.498
0.523
0.457
0.485
0.4888
0.066
6
0.472
0.496
0.502
0.495
0.505
0.494
0.033
7
0.494
0.502
0.494
0.471
0.504
0.493
0.033
8
0.505
0.499
0.486
0.472
0.487
0.4898
0.033
9
0.472
0.501
0.507
0.504
0.506
0.498
0.035
10
0.465
0.502
0.505
0.511
0.485
0.4936
0.046
11
0.495
0.495
0.456
0.494
0.491
0.4862
0.039
12
0.458
0.463
0.525
0.504
0.529
0.4958
0.071
13
0.516
0.502
0.495
0.521
0.504
0.5076
0.026
14
0.491
0.521
0.502
0.495
0.508
0.5034
0.03
15
0.493
0.505
0.487
0.511
0.503
0.4998
0.024
16
0.471
0.501
0.484
0.475
0.525
0.4912
0.054
17
0.481
0.481
0.508
0.473
0.484
0.4854
0.035
18
0.507
0.493
0.495
0.472
0.484
0.4902
0.035
19
0.501
0.539
0.494
0.485
0.493
0.5024
0.054
20
0.513
0.494
0.485
0.504
0.502
0.4996
0.028
Overall Average
(Average of 20 samples)
0.49464
0.0407
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