1. Descriptive Statistics1 LSSG Green Belt Training Descriptive Statistics

2. 2 Measures of Central Location Mean, Median, Mode Measures of Variation Range, Variance and Standard Deviation Describing Data: Summary Measures

3. Descriptive Statistics3 It is the Arithmetic Average of data values: The Most Common Measure of Central Tendency Affected by Extreme Values (Outliers) 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 5Mean = 6 Sample Mean Mean n xxx n2i   n x n 1i i    x

4. Descriptive Statistics4 0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5 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 Median

5. Descriptive Statistics5 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 Mode = 5 0 1 2 3 4 5 6 No Mode Mode

6. Descriptive Statistics6 Measures Of Variability Range and Inter Quartile Range Variance and Standard Deviation Coefficient of Variation

7. Descriptive Statistics7 Measure of Variation Difference Between Largest & Smallest Observations: Range = Highest Value – Lowest Value Ignores How Data Are Distributed: Range 7 8 9 10 11 12 Range = 12 - 7 = 5 7 8 9 10 11 12 Range = 12 - 7 = 5

8. Descriptive Statistics8 Inter Quartile Range Difference between the 75 th percentile (3 rd Quartile) and the 25 th percentile (1 st Quartile) Eliminates Effects of Outliers Captures how data are distributed around the median (2 nd Quartile) Q1 Q2Q3 IQR

9. Descriptive Statistics9 Important Measure of Variation Shows Variation About the Mean For the Population: For the Sample: Variance    2    1 2 2    n X s i  N X i    2     1 2     n XX S2S2 i

10. Descriptive Statistics10 Most Important Measure of Variation Shows Variation About the Mean For the Population: For the Sample: Standard Deviation For the Population: use N in the denominator. For the Sample : use n - 1 in the denominator.  N X i    2    1 2     n XX s i

11. Descriptive Statistics11 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  1 2     n XX s i

12. Descriptive Statistics12 Comparing Standard Deviations Mean = 15.5 s = 3.3 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s =.92 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C

13. Descriptive Statistics13 Coefficient of Variation Relative Variation (adjusted for the mean) Measured as a % Adjusts for differences in magnitude of data Comparison of variation across groups

14. Descriptive Statistics14 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%

15. Descriptive Statistics15 Shape of Distribution Describes How Data Are Distributed Measures of Shape: Symmetric or skewed Right-Skewed Left-SkewedSymmetric Mean =Median =Mode Mean Median Mode Median Mean Mode

16. Descriptive Statistics16 BOX PLOTS Captures Many Statistics in One Chart Q1 Q3 Median Mean Max Min