The ages of Kylee's five cousins are listed below. 9 12 11...

The ages of Kylee's five cousins are listed below. 9 12 11 14 6 1) Calculate the mean. $\mu =$ 2) Fill in the table below: Fill in the differences of each data value from the mean, then the squared differences. $x$ $x - \mu$ $(x - \mu)^2$ 9 12 11 14 6 $\sum (x - \mu)^2 =$ 3) Calculate the population standard deviation ($\sigma$). $\sigma = \sqrt{\frac{\sum (x - \mu)^2}{N}} = $ (Please round your

Transcript

00:01 So there's a couple different styles of questions here.

00:04 And the first one, we want to find the mean age of this frequency distribution.

00:09 So the first thing we have to do is we're going to have to find the midpoint of each of these classes.

00:17 And sometimes that's referenced as being the class mark.

00:23 Because we don't know what age the two people in the first class were.

00:30 We don't know if there was a six -year -old and a seven -year -old.

00:34 Was there a six -year -old and a ten -year -old? so by finding a class mark or a midpoint, we have a representative age of that class.

00:43 And to calculate midpoint, we add the lower class limit to the upper class limit, and then we divide by the fact that there were two pieces of data.

00:52 So if we add six plus ten, we get 16.

00:56 When we average the six and the ten together, so we divide 16 by two.

01:00 We are going to get a midpoint or a class mark of eight.

01:05 So we're going to make an assumption that there were two eight -year -olds recorded in this data.

01:11 We'll find the midpoint for 11 through 15, and that will be a midpoint of 13.

01:17 The midpoint from 16 to 20 would be 18, and the midpoint from 21 to 25 is going to be 23.

01:26 We're going to call that our x value and our frequency, we're going to use the variable f.

01:35 So in order to find the mean, we have to sum up x times f and divide by n.

01:45 So now we're going to add an additional column, and we're going to title it x times f.

01:52 So we'll take each x value times its corresponding frequency.

01:58 So 13 times 4 would be 52, 18 times 7 would be 126, and 23 times 1 would be 23.

02:08 So our formula calls for us to add up that column.

02:14 So if i add up that column, i will get 217.

02:22 And i have to divide by how many total pieces of data there were.

02:26 And if i look at my frequency column, i know that there were two, let's say, eight -year -olds, and four 13 -year -olds, an additional 7, 18 -year -olds, and one 23 -year -old.

02:42 So we have a total of 14 pieces of data.

02:49 So when i divide by 14, my mean of this frequency distribution would be 15.

02:57 15 .5 years old.

03:02 In number two, we are looking at a set of data that involves average january temperatures.

03:11 They are measured in, looks like, celsius degrees.

03:15 And we want to find the interquartile range.

03:19 And in order to calculate the iqr, or interquartile range, we have to find quartile 3 and subtract quartile 1.

03:31 So notice that the data is arranged in order from smallest to largest.

03:37 And in order to find quartile 3 and quartile 1, we're first going to have to find the middle of the data.

03:43 So since there are 11 pieces of data, our middle or our median is 4 .1.

03:50 And what this does is it separates our data so that there are five pieces of data below that median value, and there are five pieces of data above.

04:04 And then to find q1, we only look at the first half of the data, and we find the middle or the median of that first half.

04:13 So the median of the first half would be 0 .2 because there are two pieces of data below it and two above it in the first half of the data.

04:27 We'll do the same thing in the upper high...

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