Question

A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows. Find the median of the observations.

A) 69

B) 72.5

C) 72

D) 73

67	72	65	75	85
73	60	88	64	89
68	91	75	61	80
62	67	80	69	72
59	86	74	63	81

Answer 1

Here, we have given that

Xi: Age of citizens

n= number of ages of the uninsured senior citizens

Xi
67
72
65
75
85
73
60
88
64
89
68
91
75
61
80
62
67
80
69
72
59
86
74
63
81

Now, we want to find the median for the Xi,

we know that if the n (i.e. no of observation) is even ex: n=4 then the median is the average of two middle most observations after sorting the data in ascending order.

and if the n (i.e. no of observation) is odd ex: n=5 then the median is the middle most observation after sorting the data in ascending order.

Now, in our case, we have n=25 observations which is odd number

first, we sort the data in ascending order.

Xi
59
60
61
62
63
64
65
67
67
68
69
72
72
73
74
75
75
80
80
81
85
86
88
89
91

we get,

Median = 13th observation (i.e. middle most observation)

= 72

i.e. option C is correct.

we can also find the median using EXCEL software =MEDIAN(Xi).