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:


69 74 75 62 70 93 64 69 61 88 67 77 87 90 66 91 77 63 82 82 71 74 76 65 83


(a) Find the standard devation of the observations.


A. 74


B. 75.04


C. 94.95


D. 9.74


(b) Find the median of the observations. ト


A. 77


B. 74


C. 67.2


D. 83

Answer 1

Answer:

a) $s= 9.74$

D. 9.74

b) $Median= 74$

B. 74

Step-by-step explanation:

Part a

We have the following dataset given:

69 74 75 62 70 93 64 69 61 88 67 77 87 90 66 91 77 63 82 82 71 74 76 65 83

We can begin calculating the sample mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X = 75.04$

Now we can calculate the sample deviation with the following formula:

$s =\sqrt{\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}}$

And after replace we got:

$s= 9.74$

Part b

For this case we need to sort the value on increasing way:

[1] 61 62 63 64 65 66 67 69 69 70 71 74 74 75 76 77 77 82 82 83 87 88 90 91 93

And the median would be the value in the position 13 and we got:

$Median= 74$