Question

Your assignment is to do a detailed statistical analysis of the data to be able to decide later what would be appropriate control charts to monitor these variables.

The manager provides you data that the office has collected on these two variables:

• Time it takes since the patient checks-in until the patient checks-out
• Number of patients in the waiting room

Present a report to the manager with the results of the statistical analysis of the data and your conclusions on the variables that will be used to monitor the process performance.

Time it takes since the patient checks-in until the patient checks-out
Observation	Time (minutes)
1	62.14
2	57.41
3	26.73
4	42.26
5	43.74
6	74.56
7	48.13
8	86.31
9	53.24
10	53.18
11	48.11
12	36.5
13	59.61
14	54.33
15	41.55
16	41.08
17	50.88
18	69.97
19	51.74
20	38.86
21	78.41
22	33.97
23	55.05
24	26.06
25	69.2
26	34.85
27	31.95
28	40.58
29	54.27
30	25.5
31	35.31
32	47.13
33	57.26
34	60.88
35	48.04
36	52.95
37	43.4
38	33.48
39	52.89
40	25.75
41	54.07
42	44.1
43	44.7
44	62.07
45	26.47
46	36.9
47	57.39
48	66.52
49	60.59
50	40.62
51	44.68
52	43.8
53	63.47
54	39.36
55	85.98
56	41.13
57	52.86
58	44.75
59	17.26
60	43.47
61	32.6
62	44.1
63	69.64
64	79
65	59.99
66	44.93
67	51.54
68	64.99
69	37.88
70	54.02
71	49.41
72	47.66
73	73.03
74	48.88
75	72.41
76	46.14
77	65.28
78	40.46
79	44.32
80	58.42
81	100.65
82	47.51
83	43.31
84	42.62
85	73.19
86	30.77
87	55.73
88	70.71
89	65.12
90	75.82
91	36.26
92	52.59
93	49.3
94	40.8
95	51.2
96	59.28
97	27.59
98	28.02
99	28.23
100	45.74

Answer 1

Using the statistical formulae and applying to the data we can find out various kth moments so as to study the trends in the data.

Let X be the random variable representing the time taken from check in to check out.

First of all we would calculate expected time taken from the check in till check out.

E(X)= 50.27

This represents how much time on an average each patient spends in the hospital from check in to check out.

Variance

Variance tells us squared deviations from the mean i.e. how much each value in the data sets deviates from the mean or central value on an average.

Var(X)= 230.77

Standard deviation is square root of variance.

Sd=15.19

We can say that there is a large spread in the data i.e the data is not just concentrated around the mean value, rather it is spread and comprises of extreme values too (the values that deviate very much from the mean)

Median: It is the value under which the 50% of the data values lie. It basically divides the data into too parts. Probability of X taking a value more or less than the median value is 0.5

Median of the data can be found by first arranging them in the ascending order and then finding out the middle value.

M=48.12

Despite studying all these moments, the effectiveness of the process shall depend on the randomness of the sample and reliability of the data.