Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 14 senior citizens were as follows:
60
61
62
63
64
65
66
68
68
69
70
73
73
74
Determine the third quartile of the ages of the senior citizens.
74.75
77.75
70.75
84.75
To determine the third quartile of the ages of the senior citizens, we first need to organize the ages in ascending order:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74
The total number of ages is 14, so the first quartile would be at the (1/4) * 14 = 3.5th position, which is between the 3rd and 4th values. Since there is no exact middle value in this scenario, we take the average of the two middle values:
(62 + 63)/2 = 62.5
Therefore, the first quartile is 62.5.
Similarly, the third quartile would be at the (3/4) * 14 = 10.5th position, which is between the 10th and 11th values. Again, we take the average of the two middle values:
(68 + 68)/2 = 68
Therefore, the third quartile of the ages of the senior citizens is 68.