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# Quantitative Methods - Chapter 3: Measures of Central Tendency

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## Jean-Michel Sotiron

on 29 August 2016

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#### Transcript of Quantitative Methods - Chapter 3: Measures of Central Tendency

MODE
MEDIAN
MEAN
Mode
Median
Mean

Exercise
Measures of Central Tendency
Quantitative Methods Lecture IV-Chapter 3
What does this have to do with QM?
A lot of it is about wealth and income inequality
What is the average income?
Who is above it?
Who is below it?
What are measures of central tendencies?
Measures of Central Tendency
What are they?
What is the average income earned by graduates of high school vs. university?
How many cigarettes are smoked by the average teenage smoker?
How do female and male grade averages compare at cegep?
Measures of Central Tendency
The value that best represents a data set
A single element that is typical
Generally located at the centre of a distribution
Center of data distribution
Values greater than central tendency
Values lower than central tendency
Measures of Central Tendency
The average person uses them in an average way
We are not average!
Precise
Numerical
Many types:
Arithmetic mean
Median
Mode
Geometric mean
Harmonic mean
Weighted mean
Truncated mean
Midrange
Midhinge
Trimean
Winsorized mean
Are we average?
AKA
Mo
What is the mode?
It is the value that appears the Mo-st
MODE
How do you find the mode?
Inspection, not calculation
1. Put numbers in order of smallest to largest
2. Look for numbers that appear most often
Example:
My set of numbers
7, 9, 11, 6, 13, 6, 6, 3, 11
Put them in order
3, 6, 6, 6, 7, 9, 11, 11, 13
Find the most common element
MODE
Why use it?
Let's check out its characteristics
-Least precise measurement of central tendency
-Important in understanding sets of scores with fewer values that occur quite often
What level of measurement?
-Most often used with nominal data (only one)
-No formula
-You can have more than one mode. Ex: Bimodal
5, 8, 1, 78, 4, 4, 36, 17, 4, 36, 25, 36
1, 4, 4, 4, 5, 8, 17, 25, 36, 36, 36, 78
Set of numbers:
What do you do now?
MEDIAN
What is the median?
It is the middle value
What is a median in "real" life?
How do you find it?
1. Order the numbers from smallest to largest
2. Find the number in the middle of the list
My set of numbers: 7, 9, 11, 6, 13, 6, 6, 3, 11
Put them in order: 3, 6, 6, 6, 7, 9, 11, 11, 13
What's the number in the middle?
MEDIAN
Used less often than the mean
When is it useful?
Cases with extreme values
Ex: 13, 9, 27, 22, 17, 18, 20, 907
What about if there's an even number of values?
Take the average of the two middle values
Ex: 17, 8, 21, 25, 13, 15, 32, 45
What do you do?
8, 13, 15, 17, 21, 25, 32, 45
Now?
17 + 21 = 38
38/2 = 19 = MEDIAN
AKA
Mdn
MEAN
What is the mean?
It's the average. If every element were the same, what would it be?
How do you calculate it?
1. Add up all the numbers
2. Divide the sum by the number of elements
7, 9, 11, 6, 13, 6, 6, 3, 11
7 + 9 + 11 + 6 + 13 + 6 + 6 + 3 + 11
= 72
Then what?
72 / 9 = 8 = MEAN
MEAN
It is the most straight forward and widely used central tendency measure
X = ∑Xi / N
_
Remember: Formulas are like recipes
X = Mean
∑ = Sum (Sigma)
Xi = list of values
N = Number of cases (Population)
Ex: 4, 6, 5, 7
4 + 6 + 5 + 7
5.5
4, 6, 5, 7
4
= 22
22/ 4
Deviation from Mean
What does deviation "mean"?
Distance and direction from the mean
aka "How far is this number from the mean"
The greater the deviation, the greater the distance
How do you find it?
Score - mean = deviation
Penultimate set: 7, 9, 11, 6, 13, 6, 6, 3, 11
What was the mean?
8
Score - mean = deviation
What is the deviation of 3 from the mean?
(AKA How far is 3 from the mean?)
3 - 8 = -5
3 is -5 away from (and below) the mean
Comparing Mode, Median and Mean
Comparing Mode, Median and Mean
Mode
Median
Mean

Comparing Mode, Median and Mean
Comparing Mode, Median and Mean
Sometimes MODE is most useful:
With nominal data
Ex: Ethnicity
Sometimes MEDIAN is most useful:
When wanting to disregard outliers
Example: 1, 2, 3, 5, 8, 9, 10, 12, 98
Sometimes MEAN is most useful:
When we want our “average” to reflect all values in our data set
Ex: 35, 60, 65, 67, 71, 73, 74, 75, 77, 79, 80, 81, 84, 97
Mean: 72.7
Practice
Determine the mean, median, and mode for the following set of numbers:
3, 7, 5, 4, 5, 6, 7, 8, 6, 5
Mean: 5.6
Mode: 5
Median: 5.5
Video Time
What is the most common wake-up time for young adults?
Troy 22
Virginie 80
Jean-George 55
Ali 33
Christopher 31
Elizabeth 130
Toni 41
Miley 29
Nicole 22
Joshua 39
Jerome 58
Ben 80
Paul 29
Carole 33
Julia 33
(Salary in '000s)
What level of measurement is this?
If you were accountant for the union, which measure of central tendency would you use to represent salaries? Why? What would be your result?
If you were accountant for the owners, which measure of central tendency would you use to represent salaries? Why? What would be your result?
Salary negotiation time!
Median: 19
Mean: 129.125
What's this?
Let's look at a race.
Nominal
Ordinal
Scale
SCALE
Countries represented
Order

Time
Full transcript