SOME TRICKY THINGS RELATED TO STEM

AND LEAF PLOTS AND CALCULATING THE STANDARD DEVIATION AND VARIANCE OF

POPULATIONS

B Heard

(Do not copy or post without my permission, students may download one copy for

personal use)

SOME TRICKY THINGS Let’s look at two questions

The salaries of 7 randomly selected employees at Acme Inc. (in thousands) are listed as: 27,33,35,39,42,46,51

John Doe’s salary for the first 7 years of his career at Acme Inc (in thousands) was as follows: 27,33,35,39,42,46,51

On the chart that follows, there will be questions about each of these.

SOME TRICKY THINGS For both cases, do the following

1. Stem and leaf plot2. Find the mean3. Find the median4. Identify the mode5. Find the range6. Find the variance7. Find the standard deviation

SOME TRICKY THINGS

1st Question (Dealing with a

Sample)

SOME TRICKY THINGS• The salaries of 7 randomly selected

employees at Acme Inc. (in thousands) are listed as: 27,33,35,39,42,46,51Not a problem on this one because this is

“SAMPLE DATA” We can use Minitab

SOME TRICKY THINGS I simply entered the data in Minitab

SOME TRICKY THINGS For the stem and leaf plot, I simply used

Graph >> Stem and Leaf (selecting my data for graph variable)

This is not correct (there are two 3 stems and two 4 stems), so I went back in to see what caused this. I discovered I needed to put in a value of “10” for the increment because I want the stems to be the “tens digit.”

SOME TRICKY THINGS After I did this, I got the correct stem and leaf

SOME TRICKY THINGS Honestly, I like to type out my stem and leaf plots

when I am dealing with a small amount of data (10 or less)

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SOME TRICKY THINGS This is the first time I’ve ever caught this.

I’m sure there is a reason, but I think I figured out a quick fix (that I explained to you)

I still recommend just doing it by hand! Most, if not ALL of the problems you will see on quizzes and the final exam can EASILY BE DONE BY HAND.Always count your “leaves” and make sure

you have the same number as you do data points

SOME TRICKY THINGS As for the remainder of the question, I

used Minitab for the FIRST ONE. Use Stat >> Display Descriptive

Statistics

SOME TRICKY THINGS Click Statistics >> /Display Descriptive Statistics Select your data Click “Statistics button” (chart that follows)

SOME TRICKY THINGS Check/Uncheck to get what you need

SOME TRICKY THINGS Let’s answer the questions

1. Stem and leaf plot (Done)2. Find the mean (39.0)3. Find the median (39.0)4. Identify the mode (No Mode – the * means there isn’t

one)5. Find the range (24)6. Find the variance (66.33)7. Find the standard deviation (8.14)

SOME TRICKY THINGS You just need to know the buttons to

push!

Let’s look at the second question.

SOME TRICKY THINGS

2nd Question (Dealing with a

Population)

SOME TRICKY THINGS• John Doe’s salary for the first 7 years of his

career at Acme Inc (in thousands) was as follows: 27,33,35,39,42,46,51THIS IS A POPULATION SINCE IT IS THE

FIRST 7 YEARS OF HIS CAREER (WE HAVE ALL OF THE DATA) We can use Minitab for everything except the

Standard Deviation and Variance

SOME TRICKY THINGS1. Stem and leaf plot2. Find the mean3. Find the median4. Identify the mode5. Find the range6. Find the variance7. Find the standard deviation

SOME TRICKY THINGS Stem and leaf – The same as the

previous since the data is the same

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SOME TRICKY THINGS The other questions

1. Stem and leaf plot (Done)2. Find the mean (39.0)3. Find the median (39.0)4. Identify the mode (No Mode – the * means there isn’t one)5. Find the range (24)6. Find the variance (WRONG BECAUSE IT’S A

POPULATION)7. Find the standard deviation (WRONG BECAUSE IT’S

A POPULATION)

NO

SOME TRICKY THINGS Since we are dealing with a population,

the formula is different for the variance and standard deviation.

Minitab only gives you the SAMPLE VARIANCE AND STANDARD DEVIATION

SOME TRICKY THINGS Page 81- 83 in the online text

Population formulaDivides by “N” or the number of data points

NOTE THE DIFFERENCE IN THE DENOMINATORS OF THE FORMULAS

Sample formulaDivides by “n-1” or “one less” than the number of data points

SOME TRICKY THINGS There are a couple of ways you can do

this to get the variance and standard deviation correctBy hand using the formula from the textDo it in Excel

SOME TRICKY THINGS I will show you how to do it in Excel

First, simply type your data into Excel

SOME TRICKY THINGS In a different cell (below or to the right) start

typing = std (WHEN YOU DO, EXCEL WILL POP UP A LIST OF WHAT IT THINKS YOU WANT)

Select STDEVP by double clicking it

SOME TRICKY THINGS When you have done this, select your data

by left clicking and dragging from the first data point to the last.

SOME TRICKY THINGS Type a right parentheses “)” and hit enter

I see my Population Standard Deviation of 7.54

SOME TRICKY THINGS Similarly, I start typing “=var” and

select =VARP( to get the Population Variance of 56.857

I could have also squared 7.540368 (the Population standard deviation) to get the population variance

Never round until your final answerThat is why I noted 7.540368 rather than

just 7.54

SOME TRICKY THINGS So for the second problem, I had a

Population. If I had used my Minitab variance and

standard deviation, I would have missed the problem

As we know now, the correct answer was

Population Standard Deviation 7.54 Population Variance 56.86

I rounded to two decimal places for both

SOME TRICKY THINGS

Good Luck