A quality inspector took 10 different samples, each with 5 observations, of the weight of a part (in grams). Please see the data sheet for the samples and observations. Use z = 3.

1. Calculate sample means.

2. Calculate sample ranges.

3. Calculate grand mean.

4. Calculate average of sample ranges.

5. Determine x-bar chart control limits.

6. Determine R chart control limits.

7. Create x-bar chart and plot values.

8. Create R-chart and plot values.

9. Conduct a median run test on the sample means.

10. Conduct an up/down run test on the sample means.

11. Are the processes in control?

12. Are the variations random or are there any non-random patterns?

DATA

	Observations
Sample	1	2	3	4	5
1	48.01	48.04	47.95	47.98	48.05
2	48.09	48.07	47.96	47.95	47.92
3	48.02	48.08	48.10	47.99	48.00
4	48.04	47.95	48.06	48.04	47.95
5	47.90	47.98	48.05	47.89	47.99
6	48.03	47.95	47.92	47.97	48.01
7	48.05	47.96	48.02	48.08	47.96
8	47.86	47.95	47.98	48.05	47.99
9	48.12	48.01	47.95	47.92	48.02
10	47.89	47.99	47.93	48.05	47.96