Some tricky things related to using Minitab for Stem and Leaf Plots and finding the Population Variance and Standard Deviation

1. B Heard
(Do not copy or post without my
permission, students may download one
copy for personal use)

2.  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
 Onthe chart that follows, there will be
questions about each of these.

3.  For both cases, do the following
1. Stem and leaf plot
2. Find the mean
3. Find the median
4. Identify the mode
5. Find the range
6. Find the variance
7. Find the standard deviation

4. 1 Question
st
(Dealing with a
Sample)

5. • The salaries of 7 randomly selected employees at
Acme Inc. (in thousands) are listed as:
27,33,35,39,42,46,51
 Not a problem on this one because this is
“SAMPLE DATA”
 We can use Minitab

6. I simply entered the data in Minitab

7.  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.”

8.  After I did this, I got the correct stem and leaf

9.  Honestly,I like to type out my stem and leaf plots
when I am dealing with a small amount of data
(10 or less)
2| 7
3| 359
4| 26
5| 1

10.  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

11.  As for the remainder of the question, I used
Minitab for the FIRST ONE.
 Use Stat >> Display Descriptive Statistics

12.  Click Statistics >> /Display Descriptive Statistics
 Select your data
 Click “Statistics button” (chart that follows)

13.  Check/Uncheck to get what you need

14.  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)

15.  You just need to know the buttons to push!
 Let’s look at the second question.

16. 2ndQuestion
(Dealing with a
Population)

17. • 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
 THIS 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

18. 1. Stem and leaf plot
2. Find the mean
3. Find the median
4. Identify the mode
5. Find the range
6. Find the variance
7. Find the standard deviation

19.  Stem and leaf – The same as the previous
since the data is the same
2| 7
3| 359
4| 26
5| 1

20.  The other questions
NO
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)

21.  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

22.  Page 81- 83 in the online text
Population formula
Divides by “N” or
the number of
data points
Sample formula
Divides by “n-1” or
“one less” than the
number of data
points
NOTE THE
DIFFERENCE IN THE
DENOMINATORS OF
THE FORMULAS

23.  Thereare a couple of ways you can do this to
get the variance and standard deviation
correct
 By hand using the formula from the text
 Do it in Excel

24. I will show you how to do it in Excel
 First, simply type your data into Excel

25.  Ina 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)

26.  When you have done this, select your data by
left clicking and dragging from the first data
point to the last.

27.  Type a right parentheses “)” and hit enter
 I see my Population Standard Deviation of 7.54

28.  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 answer
 That is why I noted 7.540368 rather than just
7.54

29.  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

30. Good Luck