Statistics in MS Excel

Statistics in MS Excel
Industrial Quality Management Week 2
11/1/2011
Udon Thani Rajabhat University
Prof. Jeff Nash
Table of Contents
Objectives: ........................................................................................................................... 3
Statistics Using Excel .......................................................................................................... 4
Statistics Using Excel and MegaStat .................................................................................. 6
Step 1 – Get MegaStat .................................................................................................... 6
Step 2 - Adding MegaStat to Excel ............................................................................... 10
Descriptive Statistics ......................................................................................................... 13
Measures of Data Distribution........................................................................................... 16
The Normal Frequency Distribution .............................................................................. 16
Standard Deviation ........................................................................................................ 16
Mean ............................................................................................................................... 17
Median ............................................................................................................................ 17
Mode............................................................................................................................... 17
Visualizing Data ............................................................................................................. 20
Pie Charts ................................................................................................................... 20
Histograms (Bar Charts) ............................................................................................. 20
Dot Plot ....................................................................................................................... 21
Stem and Leaf Diagrams............................................................................................ 22
Box Plots ..................................................................................................................... 23
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Objectives:
The objective of this document is to provide information to allow the user to:
1. Download the MegaStat add-in from the Internet and install it in Excel.
2. Provide an overview of using Excel for descriptive statistics.
3. Provide an overview of using Excel for inferential statistics.
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คำสำคัญ
Statistics Using Excel
MS Excel has many built in statistical functions. You can see this by
clicking on the Insert Function button in your Excel worksheet.
That yields an Insert Function menu as seen next:
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From the Insert Function Menu, select statistical and click on the OK
button. This gives a list of about 50 statistical functions from which
to choose. A small fraction is shown below:
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Statistics Using Excel and MegaStat
MegaStat is an Excel plug-in that can be downloaded for free from
McGraw Hill. MegaStat is a Graphical User Interface (GUI)
through which a user can select data and analyses to run. It
makes statistical analysis in Excel very easy.
เป๊ นฟรี
และง่าบมาก
MegaStat
ต้องการไฟล์
MegaStat.xla
Step 1 – Get MegaStat
อ.เจฟ ให้สามารถ
I have a flash drive with MegaStat. You may copy the file from me.
All you need is a file called, MegaStat.xla. Place it in your file
directory and remember where.
MegaStat.xla
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Alternately you could download MegaStat from McGraw Hill. The
URL is:
http://highered.mcgrawhill.com/sites/0010126585/student_view0/megastat.html
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The information and download instructions are at the bottom of this
page. It looks like this:
Note that there is a tutorial as well.
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Click on one of the download options under “Installing the MegaStat
Add-In”. The following menu appears. Click Open.
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Then, Click Allow on the Menu below.
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Then Extract to the desktop, finally clicking on OK
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The following three (3) files are then on your desktop. MegaStat is
now on your computer (bottom file).
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Step 2 - Adding MegaStat to Excel
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In your Excel spreadsheet, click on the Microsoft Logo. The menu
below will appear. Click on Excel Options at the bottom of this
menu.
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This results in the Excel Options menu. Click on Add-Ins and then
the Go Button.
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The Add Ins menu appears. Make sure that Analysis ToolPak,
Solver Add-In and MegaStat are checked. Click OK.
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MegaStat now appears in your program under the Add-Ins menu.
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Excel and MegaStat are now correctly configured. You are ready to
use it.
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Descriptive Statistics
Descriptive statistics involves numerically or graphically
summarizing data so that it is easier to understand. I‟ll show you a
few examples.
You can use any data set. I have one that involves grades for
quizzes. Click on MegaStat under the Add-Ins menu. The following
menu appears.
Choose Descriptive Statistics. The Descriptive statistics menu is
produced as shown below.
1.
2.
3.
4.
Choose the tests that you want to run.
Click on any data point
Click on the Input range label to expand your selection.
Click on the OK button.
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Clicking OK creates a new sheet called, Output with the results of
your analysis. Notice that there are many options. A few
descriptive statistics are show and 1 dot plot. This is shown in the
next figure.
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Click on Input
range before
clicking on OK
An Output sheet is created containing the following results:
DotPlot
0
20
40
60
Quiz Grades
80
100
120
Descriptive statistics
count
mean
sample variance
sample standard
deviation
minimum
maximum
range
Quiz
Grades
21
84.19
467.56
21.62
11
100
89
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We can see that there are a lot of statistical procedures that we can
u se. Have a look at an earlier menu:
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Descriptive statistics are all under the first two (2) menu items,
Descriptive Statistics and Frequency Distributions.
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Measures of Data Distribution
The Normal Frequency Distribution
A very common way in which data are distributed is called the
normal distribution. It looks like this:
If we sample data on a specific characteristic which is normally
distributed, several important features are seen:
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1. Data are centered around the middle of the curve, Z=0
above.
2. The curve continues to +/- ∞. It never touches the horizontal
axis.
3. The areas under the curve correspond to probabilities.
4. Total area under the curve is equal to 1.0000.
Standard Deviation
The curve you see above is a standard normal curve. None of your
data will be standard. The Z values in the curve above represent
the Number of Standard Deviations from the mean. Also note that
the mean value is 0. You need a way to convert your data to
standard normal form. That is done with the following formula:
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Where: x is your value of interest;  is the mean value observe, 
is standard deviation.
Population standard deviation is given by the following formula:
where n is the number of data points. In the end, we consider
standard deviation a measure of the width the probability distribution
for a given data set.
Sample standard deviation, s, is given as:
Mean
The mean is nothing more than the average, and it is expressed as:
Median
Median is the point at which the 50% of the data has a greater value and 50% has a
smaller value. The median of a data set is found through inspection or by using
software.
Mode
The mode of a data set is its most commonly occurring value. If no value occurs at
least twice, there is no move. If several values occur with the same frequency, the data
set has multiple modes. The mode of a data set is found through inspection or by using
software.
Let‟s follow this with an example.
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Example 2.1
Given that a course is taught for two classes, the following data was
generated:
Grades
Quiz # Class 1 Class 2
1
78

2
73

3
88

4
91

5
99

6
56

7
42

8
65

9
83

10
69

Calculate the standard deviation for Class 1 as follows:
Class 1
x
78
73
88
91
99
56
42
65
83
69
Sum:
Divide by n
divide by n-1
Calc 
Calc s
(x - 
3.60
-1.40
13.60
16.60
24.60
18.40
32.40
-9.40
8.60
-5.40
(x - 
12.96
1.96
184.96
275.56
605.16
338.56
1049.8
88.36
73.96
29.16
2660.4
266.04
295.6
16.311
17.193
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Results for class 2 are as follows:
Class 2
x
77
81
69
83
59
63
78
75
81
76
Sum:
Divide by n
divide by n-1
Calc 
Calc s
(x - 
(x - 
2.80
7.84
6.80
46.24
-5.20
27.04
8.80
77.44
-15.20 231.04
-11.20 125.44
3.80
14.44
0.80
0.64
6.80
46.24
1.80
3.24
579.6
57.96
64.4
7.6131
8.025
The median for Class 1 is 75.5 while that for Class 2 is 76. Class 1
has no mode value; the mode of Class 2 is 81 (it occurs twice).
Now, please compare the mean (average) values of Class 1 and
Class 2.
Then compare the standard deviation of Class 1 and Class 2. What
do these numbers tell us? Which class did better?
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Visualizing Data
Often it is helpful if we can „see a picture of the data‟. There are
many ways to do this. I would advise using software for this. Hand
drawing is just so time consuming! It‟s also quite difficult to make
changes.
Pie Charts
These charts are a segmented circle representing relative
proportions. This is the only one of the graphics that cannot be
drawn by MegaStat. Use the chart wizard. Data for Class1 and
Class 2 are as shown.
90-100
90-100
80- <90
80- <90
70 - <80
70 - <80
60 - <70
60 - <70
Histograms (Bar Charts)
The same data are represented as histograms.
30
20
10
0
Histogram
60
Percent
Percent
Histogram
40
20
0
Class 1
Class 2
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Dot Plot
Dot plots allow you to see data on an axis as well as multiple instances of
the same values. Dot plots for Class 1 and Class 2 data are given asL
DotPlot
40
50
60
70
80
90
100
110
70
75
80
85
Class 1
DotPlot
50
55
60
65
Class 2
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Stem and Leaf Diagrams
Stem and leave diagrams are textual but have a graphical look.
Results from Class 1 and Class 2 are shown below:
Stem and Leaf plot
for
stem unit =
leaf unit =
Class 1
10
1
Frequency
1
1
Stem
4
5
Leaf
2
6
2
3
2
6
7
8
59
348
38
2
9
19
Stem and Leaf plot
for
stem unit =
leaf unit =
Class 2
10
1
Frequency
1
2
Stem
5
6
Leaf
9
39
4
7
5678
3
8
113
10
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Box Plots
Box plots give indications of standard deviation. I show these for Class 1
and Class 2 data:
BoxPlot
40
50
60
70
80
90
100
110
70
75
80
85
Class 1
BoxPlot
50
55
60
65
Class 2
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Homework
1. Given the following 10 numbers: 756, 791, 707, 743, 744, 759, 766, 781, 756,
761, determine the following:
 Sample Standard Deviation
 Range
 Mean
 Median
 Mode
You may do this with Excel, if you wish.
2. Given a process with an average completion time of 91 seconds with a
population standard deviation of 3.5 seconds, calculate the Z-values for the
following times:
 84 seconds
 98 seconds
 103 seconds
3. Given a factory line that fills 30,000 boxes per day. Each box is to be filled with
250 grams of product. The population standard deviation is 1 gram. What is the
probability of randomly selecting a box that has weight:
 250 grams? (also, how many boxes does this represent?)
 251.21 grams> (also, how many boxes does this represent?)
 < 247.36 grams (also, how many boxes does this represent?)
4. Present the data in question 1 as:
 A dot plot
 A stem & leaf diagram
 A box plot
You should use Excel for this.
Due November 14, 2554
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Appendix 1
Standard Normal
Table
Z
0
0.01
0
0
0.004
0.1 0.0398 0.0438
0.2 0.0793 0.0832
0.3 0.1179 0.1217
0.4 0.1554 0.1591
0.5 0.1915
0.195
0.6 0.2257 0.2291
0.7
0.258 0.2611
0.8 0.2881
0.291
0.9 0.3159 0.3186
1
0.3413 0.3438
1.1 0.3643 0.3665
1.2 0.3849 0.3869
1.3 0.4032 0.4049
1.4 0.4192 0.4207
1.5 0.4332 0.4345
1.6 0.4452 0.4463
1.7 0.4554 0.4564
1.8 0.4641 0.4649
1.9 0.4713 0.4719
2
0.4772 0.4778
2.1 0.4821 0.4826
2.2 0.4861 0.4864
2.3 0.4893 0.4896
2.4 0.4918
0.492
2.5 0.4938
0.494
2.6 0.4953 0.4955
2.7 0.4965 0.4966
2.8 0.4974 0.4975
2.9 0.4981 0.4982
3
0.4987 0.4987
0.02
0.008
0.0478
0.0871
0.1255
0.1628
0.1985
0.2324
0.2642
0.2939
0.3212
0.3461
0.3686
0.3888
0.4066
0.4222
0.4357
0.4474
0.4573
0.4656
0.4726
0.4783
0.483
0.4868
0.4898
0.4922
0.4941
0.4956
0.4967
0.4976
0.4982
0.4987
0.03
0.012
0.0517
0.091
0.1293
0.1664
0.2019
0.2357
0.2673
0.2967
0.3238
0.3485
0.3708
0.3907
0.4082
0.4236
0.437
0.4484
0.4582
0.4664
0.4732
0.4788
0.4834
0.4871
0.4901
0.4925
0.4943
0.4957
0.4968
0.4977
0.4983
0.4988
0.04
0.016
0.0557
0.0948
0.1331
0.17
0.2054
0.2389
0.2704
0.2995
0.3264
0.3508
0.3729
0.3925
0.4099
0.4251
0.4382
0.4495
0.4591
0.4671
0.4738
0.4793
0.4838
0.4875
0.4904
0.4927
0.4945
0.4959
0.4969
0.4977
0.4984
0.4988
0.05
0.0199
0.0596
0.0987
0.1368
0.1736
0.2088
0.2422
0.2734
0.3023
0.3289
0.3531
0.3749
0.3944
0.4115
0.4265
0.4394
0.4505
0.4599
0.4678
0.4744
0.4798
0.4842
0.4878
0.4906
0.4929
0.4946
0.496
0.497
0.4978
0.4984
0.4989
0.06
0.0239
0.0636
0.1026
0.1406
0.1772
0.2123
0.2454
0.2764
0.3051
0.3315
0.3554
0.377
0.3962
0.4131
0.4279
0.4406
0.4515
0.4608
0.4686
0.475
0.4803
0.4846
0.4881
0.4909
0.4931
0.4948
0.4961
0.4971
0.4979
0.4985
0.4989
0.07
0.0279
0.0675
0.1064
0.1443
0.1808
0.2157
0.2486
0.2794
0.3078
0.334
0.3577
0.379
0.398
0.4147
0.4292
0.4418
0.4525
0.4616
0.4693
0.4756
0.4808
0.485
0.4884
0.4911
0.4932
0.4949
0.4962
0.4972
0.4979
0.4985
0.4989
0.08
0.0319
0.0714
0.1103
0.148
0.1844
0.219
0.2517
0.2823
0.3106
0.3365
0.3599
0.381
0.3997
0.4162
0.4306
0.4429
0.4535
0.4625
0.4699
0.4761
0.4812
0.4854
0.4887
0.4913
0.4934
0.4951
0.4963
0.4973
0.498
0.4986
0.499
0.09
0.0359
0.0753
0.1141
0.1517
0.1879
0.2224
0.2549
0.2852
0.3133
0.3389
0.3621
0.383
0.4015
0.4177
0.4319
0.4441
0.4545
0.4633
0.4706
0.4767
0.4817
0.4857
0.489
0.4916
0.4936
0.4952
0.4964
0.4974
0.4981
0.4986
0.499
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