Charts for Week 1 Live Lecture for GM 533

1. Welcome! Week 1 Live Lecture/Discussion
Applied Managerial Statistics (GM533)
Lecturer: Brent Heard
Please note that I borrowed these charts from Joni
Bynum and the textbook publisher.
Thanks Joni!
I will put my touch on them (in blue) as we go along.
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2. Tonight’s Agenda
• Week 1 Terminal Course Objectives (TCOs)
• Essential Questions and Problem Types
• The Most Important Ideas in Statistics
• Getting started with Minitab
• Descriptive Statistics using Minitab
• Questions?
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3. Week 1 Terminal Course Objectives (TCOs)
• TCO A Descriptive Statistics: Given a managerial
problem and accompanying data set, construct graphs
(following principles of ethical data presentation),
calculate and interpret numerical summaries
appropriate for the situation. Use the graphs and
numerical summaries as aids in determining a course
of action relative to the problem at hand.
• TCO F Statistics Software Competency: Students
should be able to perform the necessary calculations
for objectives A through E using technology, whether
that be a computer statistical package or the TI-83,
and be able to use the output to address a problem at
hand.
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4. The Most Important Ideas in Statistics
• Central tendency (measures of center) and
dispersion (spread)
• Quantitative (numbers) and qualitative (words
and numbers with no meaning) variables
• Description and inference
• One variable versus two or more variables
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5. Selected Slides from the Text Book
• The following slides from the text book are intended
to complement the live demonstration and provide a
bridge to Module 1
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6. Population Parameters
A population parameter is a number
calculated from all the population
measurements that describes some aspect of
the population (Remember “p” goes with “p”)
The population mean, denoted , is a
population parameter and is the average of
the population measurements (Fancy letters
are used for the population)
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7. Point Estimates and Sample Statistics
A point estimate is a one-number estimate of
the value of a population parameter
A sample statistic is a number calculated using
sample measurements that describes some
aspect of the sample (“s” goes with “s”)
Use sample statistics as point estimates of
the population parameters
The sample mean, denoted x, is a sample
statistic and is the average of the sample
measurements (Plain letters for the sample)
The sample mean is a point estimate of the
population mean 7

8. Measures of Central Tendency
Mean, The average or expected value
Median, Md The value of the middle point of the
ordered measurements
Mode, Mo The most frequent value
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9. The Mean
Population X1, X2, …, XN Sample x1, x2, …, xn
x
Population Mean Sample Mean
N n
Xi xi
i=1
i=1 x
N n
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10. The Sample Mean
For a sample of size n, the sample mean is defined as
n
xi
i 1 x1 x2 ... xn
x
n n
and is a point estimate of the population mean
• It is the value to expect, on average and in the long run
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11. Example: Car Mileage Case
Example 3.1: Sample mean for first five car mileages from
Table 2.4
30.8, 31.7, 30.1, 31.6, 32.1
5
xi
i 1 x1 x2 x3 x4 x5
x
5 5
30.8 31.7 30.1 31.6 32.1 156 .3
x 31.26
5 5
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12. The Median
The population or sample median Md is a value such that
50% of all measurements, after having been arranged in
numerical order, lie above (or below) it. (The median is the
“center.”)
The median Md is found as follows:
1. If the number of measurements is odd, the median
is the middlemost measurement in the ordered
values
2. If the number of measurements is even, the median
is the average of the two middlemost measurements
in the ordered values
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13. Example: Sample Median
Internist’s Yearly Salaries (x$1000)
127 132 138 141 144 146 152 154 165 171 177 192 241
(Note that the values are in ascending numerical order from left to
right)
Because n = 13 (odd,) then the median is the middlemost or
7th value of the ordered data, so
Md=152
• An annual salary of $180,000 is in the high end, well above
the median salary of $152,000
• In fact, $180,000 a very high and competitive salary
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14. The Mode
The mode Mo of a population or sample of measurements is
the measurement that occurs most frequently
• Modes are the values that are observed “most typically”
• Sometimes higher frequencies at two or more values
• If there are two modes, the data is bimodal
• If more than two modes, the data is multimodal
• When data are in classes, the class with the highest
frequency is the modal class
• The tallest box in the histogram (The Tall Pole)
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15. Relationships Among Mean, Median
and Mode
Notice tail to
right
Notice tail to left
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16. Central Tendency By Itself Not Enough
Knowing the measures of central tendency is
not enough
Both of the distributions shown below have
identical measures of central tendency
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17. The Normal Curve
Symmetrical and bell-shaped
curve for a normally distributed
population
The height of the normal over any
point represents the relative proportion
of values near that point
Example 2.4, The Car Mileages Case
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18. The Empirical Rule for
Normal Populations
If a population has mean and standard deviation and
is described by a normal curve, then
68.26% of the population measurements lie within one
standard deviation of the mean: [
95.44% of the population measurements lie within two
standard deviations of the mean: [ 2 2
99.73% of the population measurements lie within three
standard deviations of the mean: [ 3 3
2-18
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19. z Scores (will be very important in our work
with the Normal Distribution, beginning in
Week 2 and for the entire course)
 For any x in a population or sample, the associated z
score is
x mean
z
standarddeviation
 The z score is the number of standard deviations that
x is from the mean
A positive z score is for x above (greater than) the
mean
A negative z score is for x below (less than) the
mean
2-19 19

20. Measures of Variation (Spread)
Range
Largest minus the smallest measurement
Variance
The average of the squared deviations of all
the population measurements from the
population mean
Standard Deviation
The square root of the variance
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21. The Range
Range = largest measurement - smallest measurement
The range measures the interval spanned by all the data
Example:
Internist’s Salaries (in thousands of dollars)
127 132 138 141 144 146 152 154 165 171 177 192 241
Range = 241 - 127 = 114 ($114,000)
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22. Variance
For a population of size N, the population variance 2
is defined as
N
2
xi 2 2 2
2 i 1 x1 x2  xN
N N
For a sample of size n, the sample variance s2 is
defined as
n
2
xi x 2 2 2
x1 x x2 x  xn x
s2 i 1
n 1 n 1
and is a point estimate for 2
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23. The Standard Deviation
2
Population Standard Deviation, :
2
Sample Standard Deviation, s: s s
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24. Example: Population Variance
and Standard Deviation
Population of profit margins for five big American
companies:
8%, 10%, 15%, 12%, 5%
8 10 15 12 5 50
10%
5 5
2 2 2 2 2
2 8 10 10 10 15 10 12 10 5 10
5
2
2 02 52 2 2 52
5
4 0 25 4 25 58
11 .6
5 5
2
11 .6 3.406 %
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25. Example: Sample Variance
and Standard Deviation
Example 3.7: Sample variance and standard deviation for
first five car mileages from Table 2.4
30.8, 31.7, 30.1, 31.6, 32.1 so x = 31.26
5 2
xi x
s2 i 1
5 1
30.8 31.26 2 31.7 31.26 2 30.1 31.26 2 31.6 31.26 2 32.1 31.26 2
4
s2 = 2.572 4 = 0.643
s s2 .643 0.8019
2-25 25

26. Percentiles and Quartiles
For a set of measurements arranged in increasing order,
the pth percentile is a value such that p percent of the
measurements fall at or below the value and (100-p)
percent of the measurements fall at or above the value
The first quartile Q1 is the 25th percentile
The second quartile (or median) Md is the 50th percentile
The third quartile Q3 is the 75th percentile
The interquartile range IQR is Q3 - Q1
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27. Example: Quartiles
20 customer satisfaction ratings:
1 3 5 5 7 8 8 8 8 8 8 9 9 9 9 9 10 10 10 10
Md = (8+8)/2 = 8
Q1 = (7+8)/2 = 7.5 Q3 = (9+9)/2 = 9
IQR = Q3 Q1 = 9 7.5 = 1.5
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28. Population and Sample Proportions
Population X1, X2, …, XN Sample x1, x2, …, xn
p ˆ
p
Sample Proportion
Population Proportion
n
xi
ˆ
p i =1
n
^
p is the point estimate of p
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29. Example: Sample Proportion
Marketing Ethics Case
117 out of 205 marketing researchers disapproved
of action taken in a hypothetical scenario
X = 117, number of researches who disapprove
n = 205, number of researchers surveyed
X 117
Sample Proportion: ˆ
p 0.57
n 205
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30. Getting Started with Minitab
• Course Home: Minitab
• Tutorial
• Download
• Getting help with your Minitab installation
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31. Summary of Descriptive Statistics using Minitab
(concluded)
• Central tendency: mean, median, mode
• Dispersion: Range, standard deviation,
interquartile range
• Stem – and - leaf display
• Histogram and frequency distribution
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32. Essential Questions and Problem Types
for the Week 1 Mastery Module
• For a given data set, use Minitab to find
numbers, pictures, and tables which show the
central tendency, including: the mean,
median, and mode, and the skewness
• For a given data set, use Minitab to find
numbers, pictures, and tables which show the
variability, or dispersion, including: the range,
the standard deviation the interquartile range,
and the Empirical Rule
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33. Closing
I will post a link to these charts where I hang out on the internet.
I call it the “Statcave.”
http://www.facebook.com/statcave
YOU DO NOT HAVE TO BE A FACEBOOK PERSON TO SEE THE
LINKS. I DO IT BECAUSE IT’S FREE AND FUN.
In my spare time, I write a syndicated column (humor, life, feel
goods, etc.) that appears in newspapers and magazines in the
southeast. If you ever get bored, check it out at:
http://www.cranksmytractor.com
See you next week! Same Stat Time, Same Stat Channel.
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