Health care issues are receiving much attention in both...

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 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92 a. what type of shape does the distribution of the sample appear to have? [2] b. calculate the variance of the ages of the senior citizens correct to the nearest hundredth of a year squared. [4] c. determine the first quartile of the ages of the senior citizens. [2]

Transcript

00:01 Alright, so here we have some data points that we are looking for for people whose ages are here's their ages and they're too basically rich to qualify for medicaid and so the first thing we want to do is look at the shape of the distribution in order to look at the shape we're gonna want to make some kind of a simple graph probably the easiest is just to do a histogram so or even like a doll plot so i'm just going to make a close quick little dot plot here.

00:43 We're just going to go like this, right? here's 65, 75, 75, 85, 95, 90, 95.

00:53 Okay, and i'm just going to go ahead and plot the dots, kind of there where they go, just to see very quickly what the distribution looks like.

01:04 Right, so here let's go ahead and put all numbers between 60 and 65.

01:09 So there's one, i guess i'm really not doing a doll plot, i'm really doing a histogram.

01:15 And there's one, two, three, four, five numbers.

01:19 So i'm going to make that be five.

01:27 One, two, three, four, five people between 60 and 65.

01:34 And then 65 to 70, i've got one, two, three, four, five as well.

01:41 Okay, so there you go.

01:44 70 to 75, but not including 75, i've got 1, 2, 3, 4.

01:51 Okay, so i'm going to go right there to 4.

01:54 75 to 80, i've got 1, 2, 3.

01:58 Okay, so going up to 3 right there.

02:01 80 to 85, i've got 1, 2, 3.

02:06 85 to 90, i've got 1, 2, 3.

02:12 And then 90 and above.

02:20 I've got just a little bit more than that, right? i've got like two more.

02:28 Okay, so i have my distribution and this is skewed to the right, right? so that would be the shape as it is skewed right.

02:45 In order to calculate the variance, we are going to go ahead and first find the average of all these data points.

02:51 So to find the average, you just add the mold together and then divide by how many you have.

02:56 All right, so i'm going to just do this in my calculator very quickly.

02:59 60 plus 61, plus 62, plus 63, plus 64, plus 65, plus 66, plus 66, plus 66, plus 68, plus 68, plus 69, plus 70, plus 70, plus 73, plus 74, plus 74, plus 76, plus 85, plus 76, plus 81, plus 82, plus 86, plus 87, plus 89, plus 90, plus 90, plus 92.

03:24 Okay, and that gets me 1 ,000, so sorry, i'm finding the average here.

03:32 That gets me 1 ,851, and then i have to divide by how many there are, and there are 25 numbers...

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