Measures of Central Tendency and Measures of Dispersion

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Measures of Central Tendency and Measures of
Dispersion
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Measures of Central Tendency

• The aritmetic mean
• 1. on population
• 2. on sample
• The geometric mean (G)
• The harmonic mean (H)
• The median
• The mode

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Measures of Dispersion

• The Variance
• 1. on Population
• 2. on Sample
• The Standard Deviation
• 1. on population
• 2. on sample

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The Aritmetic Mean on Population for Single Data
Example
Data 0, 2, 5, 2, 1, 6, 4, 3, 4, 2
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The Aritmetic Mean on Sample for Single Data
Example
Data 0, 2, 5, 2, 1, 6, 4, 3, 4, 2
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The Aritmetic Mean on Population for Grouping Data
where
f is class frequency
X is the middle class
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The Aritmetic Mean on Population for Grouping Data
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The Geometric Mean
Example
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The Harmonic Mean
Example
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The Median for Single Data
Example
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The Median for Grouping Data
Median class
Example
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The Mode for Single Data

• Mode is the values which occur with the greatest
  frequency
• Example 3, 4, 6, 5, 4, 1, 3, 3, 2, 7,
  5
• The Mode is 3
• Example 4, 3, 5, 1, 3, 4, 6, 7, 8, 4,
  3, 1
• The Modes are 3 and 4
• Example 2, 3, 5, 4, 6, 4, 3, 2, 6, 5
• No Mode

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The Mode for Grouping Data
Example
Modus Class
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The Variance for Single Data on Population
Definition
Computation Formulae
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The Variance for Single Data on Sample
Definition
Computation Formulae
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The Variance for Grouping Data on Population
Definition
Computation Formulae
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The Variance for Grouping Data on Sample
Definition
Computation Formulae
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VARIANCE
SAMPLE
POPULATION