LSSG Green Belt Training

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LSSG Green Belt Training
Descriptive Statistics
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Describing Data Summary Measures
Measures of Central Location Mean, Median,
Mode Measures of Variation Range,
Variance and Standard Deviation
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Mean

• It is the Arithmetic Average of data values
• The Most Common Measure of Central Tendency
• Affected by Extreme Values (Outliers)

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Sample Mean
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0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12
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Mean 5
Mean 6
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Median

• Important Measure of Central Tendency
• In an ordered array, the median is the middle
  number.
• If n is odd, the median is the middle number.
• If n is even, the median is the average of the 2
  middle numbers.
• Not Affected by Extreme Values

0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12
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Mode

• A Measure of Central Tendency
• Value that Occurs Most Often
• Not Affected by Extreme Values
• There May Not be a Mode
• There May be Several Modes
• Used for Either Numerical or Categorical Data

0 1 2 3 4 5 6
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Measures Of Variability
Range and Inter Quartile Range Variance and
Standard Deviation Coefficient of Variation
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Range

• Measure of Variation
• Difference Between Largest Smallest
• Observations
• Range Highest Value Lowest Value
• Ignores How Data Are Distributed

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Inter Quartile Range

• Difference between the 75th percentile (3rd
  Quartile) and the 25th percentile (1st Quartile)
• Eliminates Effects of Outliers
• Captures how data are distributed around the
  median (2nd Quartile)

Q2
Q3
Q1
IQR
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Variance

• Important Measure of Variation
• Shows Variation About the Mean
• For the Population
• For the Sample

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Standard Deviation

• Most Important Measure of Variation
• Shows Variation About the Mean
• For the Population
• For the Sample

For the Population use N in the denominator.
For the Sample use n - 1 in the denominator.
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Sample Standard Deviation
For the Sample use n - 1 in the denominator.
Data 10 12 14 15 17 18
18 24
n 8 Mean 16
Sample Standard Deviation 4.24
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Comparing Standard Deviations
Data A
Mean 15.5 s 3.3
11 12 13 14 15 16 17 18
19 20 21
Data B
Mean 15.5 s .92
11 12 13 14 15 16 17 18
19 20 21
Data C
Mean 15.5 s 4.57
11 12 13 14 15 16 17 18
19 20 21
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Coefficient of Variation

• Relative Variation (adjusted for the mean)
• Measured as a
• Adjusts for differences in magnitude of data
• Comparison of variation across groups

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Comparing Coefficient of Variation

• Stock A Average Price last year 50
• Standard Deviation 5
• Stock B Average Price last year 100
• Standard Deviation 5

Coefficient of Variation Stock A CV
10 Stock B CV 5
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Shape of Distribution

• Describes How Data Are Distributed
• Measures of Shape
• Symmetric or skewed

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BOX PLOTS
Captures Many Statistics in One Chart
Mean
Max
Min
Median
Q1
Q3