1. (30 points) 30 students took the probability course...

1. (30 points) 30 students took the probability course midterm exam in last year. A stem-and-leaf plot of the 30 scores are shown below. The first column is the stem value, and the second colum is the leaves. Answer the following questions. Important note: Show your work. Provide the expressions and your approach on answering the questions. Results without supporting work will not be credited. Stems Leaves 3 4 5 79 6 03688 7 26799 8 1245667788 9 1234788 (a) What is the value of the first quartile? Q1 = (b) What is the value of the third quartile? Q3 = (c) What is the interquartile range? IQR = (d) Find the lower fence. (e) Find the upper fence. (f) Construct a boxplot for this data. (g) Does the boxplot indicate the presence of any outliers?

Transcript

00:01 This stem and leaf plot represents 30 students that took a probability midterm exam in the last year.

00:07 And we want to determine the first quartile.

00:12 So before we can find that first quartile, we will have to find our median.

00:16 And our median is the middle of the data.

00:20 So since there are 30 pieces of data, the middle would be where there's 15 pieces of data in front of it and 15 pieces of data after it.

00:31 So our median is going to be between these two values.

00:37 So if you count the leaves before that location, you'll see 15.

00:46 And if you count the leaves after that, you'll also see 15.

00:52 So now we're ready to find our first quartile.

00:56 And we're going to use the abbreviation q1.

00:59 And it's going to be the median of the first half of data.

01:04 So again, if you think about the first half of the data, having 15 pieces of data, then we could have seven pieces of data, then one piece of data, and then seven pieces of data.

01:17 So in essence, it's the eighth piece of data.

01:20 So if i count eight from the beginning of the list, quartile one would be the number 68.

01:32 Now we want to find quartile 3.

01:36 And the same thing, if the upper half of the data has 15 pieces of data, then again, we could think in terms of the fact that the upper half has 7, 1, and 7.

01:51 So we want the eighth piece of data from the top.

01:55 So 1, 2, 3, 4, 5, 6, 7, 8th piece of data from the top would make q3 being an 88.

02:05 Next, we want to find the iqr or the interquartile range.

02:10 And to find the iqr, you're going to subtract q3 minus q1.

02:19 So the interquartile range would be 88 minus 68 or a value of 20.

02:27 Next, we want to find the lower fence.

02:30 And your lower fence is the boundary line.

02:34 For outliers, and we find our lower fence by taking quartile 1 and subtracting 1 .5 times your interquartile range.

02:45 So our q1 or quartile 1 was 68 minus 1 .5 of the iqr, which is value of 20, we'd have 68 minus 30 or 38 is the lower fence...

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