1. Given the following data Stem Leaf 1 12677 2 1224488 3...

1. Given the following data Stem Leaf 1 12677 2 1224488 3 355666 8 456 9 68 1) (5 Points) Find the quartiles: $Q_I$, $Q_{II}$ and $Q_{III}$. 2) (5 Points) Find: the 1.5 × IQR Rules "[$Q_1$ - 1.5 × IQR, $Q_3$ + 1.5 × IQR]" and all outliers. 3) (5 Points) Draw the box plot.

Transcript

00:01 You have a stem and leaf display of some data set, and our first goal is to calculate the fourth spread.

00:09 And then we want to construct a box -in -whisker plot.

00:12 So what we're going to do here is we're going to find the five -number summary first.

00:24 And the five -number summary includes the minimum, the lower -fourth boundary, and sometimes that's represented as quartile one, the median, that is often referenced as quartile two.

00:59 The upper fourth boundary, oftentimes referenced as quartile three, and the maximum.

01:19 So we're dividing this data set into fourths.

01:23 And if you count up how many there were, there were 44.

01:28 So that means halfway would be 22.

01:34 So the halfway point would be right here.

01:38 There's 22 numbers or values before that line, there are 22 values after that line.

01:45 And then if we divide up the first 22, that means there would be 11 in front of this line and 11 after that line.

01:58 And then if we break the upper half into halves, we would have 11 before this line and 11 after that line.

02:10 So therefore, our five number summary, we have a minimum value of 32 .1.

02:20 We have a lower fourth quarter boundary by averaging these two values together.

02:28 So if i average 35 .8 and 35 .8, i will get 35 .8.

02:37 The median is the middle number.

02:40 So that means i have to average these two values together.

02:44 So if i average 36 .8 with 37 .2, i will get 37.

02:54 The upper fourth boundary, i need to average these two values together, and i will get 39 .55, and then the maximum value is 42 .9.

03:13 So i'm now ready to talk about the fourth...

Question

1. Given the following data Stem Leaf 1 12677 2 1224488 3 355666 8 456 9 68 1) (5 Points) Find the quartiles: $Q_I$, $Q_{II}$ and $Q_{III}$. 2) (5 Points) Find: the 1.5 × IQR Rules "[$Q_1$ - 1.5 × IQR, $Q_3$ + 1.5 × IQR]" and all outliers. 3) (5 Points) Draw the box plot.

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