1. Summary of Prev. Lecture
Central Tendency
Mode
Highest frequency with Nominal or Category data
Median
Middle value that can avoid outliers' influence
Mean
Arithmetic Mean: First and Second Moment
Geometric Mean
Weighted Mean

2. Distribution Descriptor 2
Geography Jinmu Choi
Measure of Dispersion (2)
Range and Percentile (2)
Mean Deviation, Variance, Std. Dev. (3)
Weighted Var. and Std. Dev., CV (3)
Skewness and Kurtosis (2)
Summary and Next…

3. Dispersion
Dispersion: How the values are concentrated or scattered around the mean and along the value line
Very similar to the mean
Quite different from the mean
Just scattered around
Xa: 1, 3, 5, 7, 9, 11, 13: Mean =
Range =
Xb: -11, -5, 1, 7, 13, 19, 25: Mean =

4. Dispersion Measures Magnitude of dispersion Direction and Sharpness
Range: Maximum – Minimum
Percentiles
Mean deviations
Standard deviations
Direction and Sharpness
Skewness
Kurtosis

5. Range Range: Maximum – Minimum Xb: -11, -5, 1, 7, 13, 19, 25 : Mean =
The greater the range in a data series, the more dispersed the data are
Only how far the values are scattered
Xb: -11, -5, 1, 7, 13, 19, 25 : Mean =
Range =
Xc: -11, -10, 6, 7, 8, 24, 25: Mean =

6. Percentiles Milestones within the range of data
Sorting and counting ¼, ½, ¾ of the total observations from the minimum
Medium = ½ from the minimum = 50%
Xb: -11, -5, 1, 7, 13, 19, 25 : Mean =
Range =
Percentile
Xc: -11, -10, 6, 7, 8, 24, 25: Mean =

7. Mean Deviation Dispersion using all values
The average difference from all values to their mean
Xa: 1, 3, 5, 7, 9, 11, 13:
Mean Dev. =
Xb: -11, -5, 1, 7, 13, 19, 25:
Mean Dev. =
Only concern the distance of the values from the mean, not the direction
M.:5 M.Dev. = 2.22…
M.:6 M.Dev. = 3.33…

8. Variance Squared difference from the mean Population variance
Sample variance

9. Standard Deviation Averaged squared deviation
The magnitude or scale of the original dataset
Mean: , Var.: , Std. Dev. :
Resembling Normal distribution with Standard Dev.
About 68% of the data value:
About 95% of the data value:
About 99% of the data value:
M.:5 Std.Dev. = 2.58…
M.:6 Std.Dev. = 4.76…

10. Weighted Variance Variance for grouped data
Get the range for each group (class)
Get mid value for each group (class)
Put mid value for each observation
Calculate variance using list of mid values
Range
4~50
50~200
200~1000
Mid value 27
125
600

11. Weighted Standard Deviation
Square root of weighted variance
Unweighted Vs. Weighted statistics
Unweighted variance:
Unweighted std. dev.:
Weighted variance:
Weighted std. dev.: 39.21
Why they are differ?
Variations in each group
have been removed

12. Coefficient of Variation
Problem of Mean, Variance: Sensitive to scale
Standard deviation
Coefficient of variation
To check just scale difference between two datasets
Mean: the center of the data
Standard deviation: how much dispersion the data have
Both (CV): difference in magnitude for comparing multiple datasets
X: : mean 7, std. dev.: 4
Y: : mean 70, std.dev.: 40

13. Skewness
Third moment statistic: Directional bias of the distribution of the data
Use frequency distribution (histogram)
X axis: numerical range
Y axis: frequency
Positive skewness
Bulk < Mean
Negative skewness
Mean < Bulk

14. Kurtosis
Fourth moment statistic: Sharpness of the distribution of the data
Use histogram
X axis: numerical range
Y axis: frequency
Kurtosis of normal dist.: 3
Normal distribution: K=0
High Kurtosis (sharp peak): K>0
Low Kurtosis (flat): K<0

15. Summary Dispersion Direction and Sharpness Range: gives boundary
Percentile: gives clustering of observation
Mean Deviation: magnitude of dispersion
Variance and Standard Deviation: magnitude of dispersion
Weighted Variance and Standard Deviation: dispersion of grouped values
Coefficient of Variation: removes scale differences
Direction and Sharpness
Skewness: direction from mean
Kurtosis: sharpness compared to normal distribution

16. Next Lab3: Additional Statistics and MAUP
Lecture 4: Relationship Descriptor 1.
Correlation Analysis
(Ch 3, pp )