Transcript Measures of Central Tendency

Measures of Central
Tendency
Mean, Median, and Mode
Measures of Central Tendency
Typical or representative number
 Condenses many numbers into one
 Typifies the middle of a set of data
 Commonly used measures of central
tendency
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Mean
Median
Mode
The Arithmetic Mean
Usually called the mean
 Most familiar measure of central
tendency
 Good choice when data are more or less
evenly distributed from lowest to the
highest values
 Calculation:

Add all of the individual values
 Divide the sum by the number of individual
values

Mean Example #1
(New customers recruited last month)
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Department #1 -- 10
agents
Agent
Number
1
18
2
3
4
5
6
7
8
9
10
19
20
20
20
20
20
22
24
28
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Sum = 18 + 19 + 20 +
20+ 20+ 20 + 20 + 22 +
24 + 28 = 211
Mean =
211 ÷ 10 = 21.1
Reasonable as a “typical”
or “middle” new customers
recruited
Mean is a reasonable
measure of central
tendency
Mean Example #2
(new customers recruited last month)
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Department #2 -- 10
agents
Agent
Number
1
18
2
3
4
5
6
7
8
9
10
19
20
20
20
20
20
22
24
120
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Sum = 18 + 19 + 20 +
20+ 20+ 20 + 20 + 22 +
24 + 120 = 303
Mean =
303 ÷ 10 = 30.3
Does NOT seem to be
“typical” or “middle”
number
No one in department is
close to 30.3
Mean is NOT a reasonable
measure of central
tendency
The Median
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Simply means “middle”
Numerically, the middle value
Is NOT influenced by extremely high or low
numbers in a set of data
Calculation:
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
Put the individual values in numerical order -- small
to large
Count the number of values in the data set
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
If odd number = middle value
If even number = halfway between the two
middle values
Median = (n+1)/2th data value
Median Examples
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Age in years of
seven security staff.
Staff Age
1. Bill
23
2. Joe
23
3. Sally
28
4. Lee
30
5. Kim
38
6. Jim
58
7. Pat
63
7 pieces of data -- odd number
7 + 1 = 8  2 = 4th data value
Median = 30 years of age
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Minutes on phone taking
orders last week.
Order # Minutes
1
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1
2
2
3
5
4
7
5
9
6
9
7
11
8
28
8 pieces of data -- even number
Two middle values = 7 and 9
Average of 7 and 9 = (7+9) ÷ 2 = 8
Median = 8 minutes
The Mode
Any value which occurs more frequently
than the others
 Most frequent or most common value
 Most appropriate when numerical
values in a data set are labels for
categories (nominal)
 Calculation:

Put the individual values in numerical order
-- small to large
 Note the value which occurs the most
frequently = Mode

Mode Examples
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Number of days late for
work for 10 security
personnel last year.
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Officer Days Absent
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1
1
2
3
4
5
6
7
8
9
10
5
Mode = 8
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6
8
8
8
11
12
12
30
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Number of vacation days
taken by 10 security
personnel last year.
Officer
Days Absent
1
3
2
3
4
5
6
7
8
9
10
5
6
10
10
10
12
15
15
15
Mode = 10 and 15
Two modes = bimodal
Choosing Measures of Central
Tendency
Measures
Mean
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Median
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Mode
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Best Uses
Interval or ratio data
Near normal distribution
Ordinal, interval, or ratio
data
Skewed distribution
Nominal, ordinal, interval,
or ratio data
Bimodal distribution
Range

The difference between the greatest and
least values in a set of data.
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The range of the data 7, 9, 15, 3, 18, 2,
16, 14, 14, 20 is computed 20-2=18
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Range is not a measure of central
tendency. It is a measure of dispersion…
it is how far the data values are spread.
Outlier
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A data value that is much higher or much
lower than the other data values in a
collection of data.

An outlier in the data 1, 2, 3, 2, 1, 51, 3,
6, 22 is 51.
Questions and
Comments
Why do you think barriers in
highways are called medians?