Question

1) From the data table given, compute the population standard deviation, ?.
2) From the data table given, compute the Upper Control Limit for s (UCLs)
3) From the data table given, compute the centerline, Xbar-bar.
4) From the data table given, compute the Average of s values, sbar.
5)Calculate the Upper Control Limit, UCLXbar
6) From the data table given, compute the Lower Control Limit, LCLXbar

This table was all the information given. I was wondering if I was missing some information. Are any of these questions answerable with just the information given?

1	74.030	74.002	74.019	73.992	74.008
2	73.995	73.992	74.001	74.011	74.004
3	73.998	74.024	74.021	74.005	74.002
4	74.002	73.996	73.993	74.015	74.009
5	73.992	74.007	74.015	73.989	74.014
6	74.009	73.994	73.997	73.985	73.993
7	73.995	74.006	73.994	74.000	74.005
8	73.985	74.003	73.993	74.015	73.988
9	74.008	73.995	74.009	74.005	74.004
10	73.998	74.000	73.990	74.007	73.995
11	73.994	73.998	73.994	73.995	73.990
12	74.004	74.000	74.007	74.000	73.996
13	73.983	74.002	73.998	73.997	74.012
14	74.006	73.967	73.994	74.000	73.984
15	74.012	74.014	73.998	73.999	74.007
16	74.000	73.984	74.005	73.998	73.996
17	73.994	74.012	73.986	74.005	74.007
18	74.006	74.010	74.018	74.003	74.000
19	73.984	74.002	74.003	74.005	73.997
20	74.000	74.010	74.013	74.020	74.003
21	73.982	74.001	74.015	74.005	73.996
22	74.004	73.999	73.990	74.006	74.000
23	74.010	73.989	73.990	74.009	74.014
24	74.015	74.008	73.993	74.000	74.010
25	73.982	73.984	73.995	74.017	74.013

Answer 1

The table represents 5 different samples (k) having 25 observation (N) each. So first of all we have to find the mean and standard deviation for each sample that is using data from each column provided in table.

The basic equations to calculate the mean and standard deviation is

So the mean and standard deviation for the given table is

S = [ 0.0116 0.0115 0.0105 0.0085 ] // Answer 1

= [   73.9995 74.0000 74.0012 74.0033 ]

for average of stanndard deviation and mean of all samples we can use the following equations

So we can calculate the following values too for the overall observations which is

74.0010

0.0105 // Answer 4

To find out the upper limit and lower limits of x bar and s bar we need to use X-S CONTROL CHART CONSTANTS which can be found anywhere on web. I am providing you the concerned data of that table

n	B_4	B_3	A_3	C_4
25	1.435	0.565	0.606	0.9896

UCL and LCL for s bar cal be calculated using the following equations

Therefore using the data from control charts constants for the  X-schart and the calculated values of , we can compute the UCLs and LCLs as

UCLs = 1.435 x 0.0105

UCLs = 0.0151 // Answer 2

Similarly LCLs = 0.565 x 0.0105

LCLs = 0.0059

The same thing goes for x bar too where UCLx and LCLx can be computed by

So UCLx = 74.0010 + 0.606 x 0.0105

UCLx = 74.0074 // Answer 5

LCLx = 74.0010 - 0.606 x 0.0105

LCLx = 73.9946 // Answer 6

Center line of x bar can be calculated my finding the midpoint of UCLx and LCLx which is

Centrelimit = 74.0010 // Answer 3

I have provided you all the steps and the final answers. Please let me know if you were stuck somewhere