Download Mean

S519: Evaluation of
Information Systems
Social Statistics
Ch2: Mean
This week
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Mean
Median
Mode
What is average
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Once the data are collected, next step is how
to organize the data
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What is the central tendency of your data
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Average (group of data can be summarized by
average)
Average is the one value that best represents an
entire group of scores
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Mean
Median
Mode
Mean
___
X
X


___
X (x bar): the mean
 X : sum of the data
n : number of the data
n
Lab
Calculate mean
Location
Number of annual customers
Lanham Park Store
2150
Williamsburg Store
1534
Downtown Store
3564
The mean or average number of shoppers in
each store?
Using Excel to do that
• use your own formula
• use AVERAGE function
Mean
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The sample mean is the measure of central
tendency which can approximate the
population mean
The mean is very sensitive to extreme scores
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It can put the mean in some extreme direction
Make it less representative
Less useful as a measure of central tendency
Lab
Weighted mean
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See Table9.10 (D-p175)
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Do it in Excel
Median
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It is defined as the midpoint in a set of scores
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50% of the scores fall above and one half fall
below.
Calculate median
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Odd number of data
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Rank them
Median=middle one
Example: 10, 9, 8, 7, 5 (median=8)
Even number of data
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Rank them
Median= sum of two middle data/2
Example: 10, 9, 8, 7, 6, 5 (median=(8+7)/2=7.5)
Lab
Median in Excel
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Calculate the median of income level
Median
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The median is insensitive to extreme cases,
where the mean is not.
To measure the central tendency:
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Have some extreme data, using median
No extreme data, using mean
Example: 14, 3, 2, 1, (mean=5, median=2.5)
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Which represents better the central tendency?
Mode
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The mode is the value that occurs most
frequently.
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Calculate the frequency of all the values in a
distribution
The value that occurs most often is the mode
Lab
Calculate mode
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300 students:
Student distribution
Number or frequency
American student
150
Asian student
30
European student
5
Mode = american student
Summary
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The mean is the middle point of a set of
values,
The median is the middle point of a set of
cases
The median cares about how many cases,
not the values. So the extreme values don‘t
count.
When to use what
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Mean:
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Median
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No extreme scores and are not categorical
Extreme scores and you do not want to distort the
average
Mode
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Data are categorical in nature and values can
only fit into one class
E.g. hair color, political affiliation, religion
Lab
Descriptive Statistics in Excel
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Take Figure2.9 (S-p57), input these figures to
Excel
Data  data analysis  data analysis box 
choose Descriptive Statistics  tick “labels in
first row”  output range=c1  tick
“summary statistics”  click “OK”
Lab
Descriptive Statistics
Income Level
Income Level
$135,456
$54,365
$37,668
$34,500
$32,456
$25,500
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
53324.16667
16887.71824
36084
#N/A
41366.2926
1711170163
4.861219327
2.173756462
109956
25500
135456
319945
6
Lab
Exercise 1 (S-p62)
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Calculate mean, median and mode for the
following data:
Score1
Score2
3
7
5
4
5
6
7
8
6
5
34
54
17
26
34
25
14
24
25
23
Score3
154
167
132
145
154
145
113
156
154
123
Lab
Exercise 2 (S-p62)

Writing a sale report to your boss according
to the figures of things sold today:
special
Number Sold
Huge Burger
Baby Burger
Chicken Littles
Porker Burger
Yummy Burger
Coney Dog
cost
20
18
25
19
17
20
$2.95
$1.49
$3.50
$2.95
$1.99
$1.99
Lab
Exercise 4 (S-p63)
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Calculate the average sale
toy
slammer
radar zinger
lazertags
Julysale AugustSale SeptemberSale
12345.00 14453.00
15435.00
31454.00 34567.00
29678.00
3253.00
3121.00
5131.00
Lab
Exercise 5 (S-p63)
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Patient record
Mean and median, which is better for what?
12/1-12/7
0-4 years
5-9 years
10-14 years
15-19 years
12
15
12
38
12/8-12/15 12/16-12/23
14
15
12
14
24
21
12
19
Stat Homework 1
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S-p62‐63: 2, 4, 5
Due Jan 28 – week3
How to submit:
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Softcopy: Oncourse
Print copy:
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write your name, email, and S519 in the first page
Submit to me during the class – week 3 (Jan 28)