Week 1 3 Extra Homework Examples (3x9)/WMA 221 Statistics for Decision Making

Professor Brent HeardNot to be copied or linked to without my permission 3 x 9

WS4DM

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•As noted, this term I will post three additional homework examples by 9 PM (Mountain Time) on Wednesday evening in the Statcave.

•(3x9)/W just means “3 by 9 PM on Wednesday.”

•This week, I will do problems similar to number 18, 22 and 24.

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•Number 18 is a basic “Find the range, mean, variance and standard deviation” type problem. I will show you how to do one in Minitab easily.

•Please note that I change the numbers so I don’t give the exact homework problem.

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•Example for 18▫Find the range, mean, variance and

standard deviation of the sample data set.9 12 5 13 12 10 9 17 11

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•First go to Minitab (I access Minitab by going to the iLab link under Course Home and then follow the “Go to Citrix” link.)

•This term there seems to be a little different look to it, but I still found Minitab in the Apps easily.

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•Enter the data in the spreadsheet part of Minitab. I labeled mine “Data for Example 1”

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•At the top of Minitab, go to Stat >> Basic Statistics >> Display Descriptive Statistics

Put your cursor in the Variables box and click, then choose/double click C1 on the left

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•Now it should look similar to this based on what you called your data

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•Click the Statistics button and select/check what you need from the menu that pops up…

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•Click your OK buttons… and you will see your answers in the Session Window

So the Mean is 10.89, Standard Deviation is 3.30, Variance is 10.86 and Range is 12. Always make sure you round correctly if asked to do so. For example, if they asked you to round to Two Decimal Places, you would notethe range as “12.00” just to be sure. Normal rounding rules apply.

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•Number 22 is a box and whisker plot type problem and is actually very easy.

•By looking at a box and whisker plot, you are asked to identify (a) the minimum, (b) the maximum, (c) the first quartile, (d) the second quartile, (e) the third quartile and (f) the interquartile range.

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•Example box and whisker plot (answers in red)

                                                                                                                                                                                                                                                               

28 30 32 34 36

29 30 33 35 36.5

Minimum

First Quartile

Second Quartile

ThirdQuartile

Maximum

Therefore, as I have labeled them, theMinimum is 29Maximum is 36.5First Quartile is 30Second Quartile is 33 (and is also the “Median”)Third Quartile is 35

The only thing that isn’t obvious is the “Interquartile Range” which is simply the Third Quartile minus the First Quartile or for this one, it would be35-30 or “5”

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•Number 24 is a histogram where we are matching z scores to a place on the histogram.

•Don’t let this one worry you, it’s actually very intuitive and easy.

•Let’s look at an example.

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•Let’s say they want us to identify points A, B and C with z scores. Our choices are:

31 36 41 46262116

A B C

z = 0z = -1.88z = 3.20

Answers next page

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•Let’s say they want us to identify points A, B and C with z scores. Our choices are:

31 36 41 46262116

A B C

z = 0

Why?Think about it…A z score of zero means you are right onthe mean. Look where B is and the shape of the histogram. It looks very symmetrical, thus the mean would be toward the middle.

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•Let’s say they want us to identify points A, B and C with z scores. Our choices are:

31 36 41 46262116

A B C

z = -1.88

Why?Think about it…A negative z score means you are thatmany standard deviations “below” themean. So with this close to symmetrichistogram, it would be on the “left” side.

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•Let’s say they want us to identify points A, B and C with z scores. Our choices are:

31 36 41 46262116

A B C

z = 3.20

Why?Think about it…Positive z scores are that many standard deviations “above” the mean.So it has to be on the right side.

(3x9)/W• Last question, “Are there any z scores that are

unusual?”

• YES, the z score of 3.20 would be considered unusual because it is more than two standard deviations away from the mean.

• z scores less than -2.00 (for example -2.02, -3.11, etc.) or greater than 2.00 (for example 2.14, 2.01, 4.19, etc.) are “MORE than two standard deviations away from the mean)

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•Hope you enjoyed this…•More examples next week….