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Descriptive Statistics
Help summarize and organize data
Used in various fields like business, medicine, and research
Mean
The average of all values
Affected by outliers (non-resistant measure)
Median
The middle value when data is ordered.
If odd, middle number
If even, average of the two middle numbers
Not affected by extreme values (resistant measure)
Mode
The most frequently occurring value
Can be unimodal, bimodal, or multimodal
Measures of Central Location
Quartiles
Deciles
Percentiles
Quartiles
Divide data into 4 equal parts (Q1, Q2, Q3)
Deciles
Divide data into 10 equal parts (D1-D9)
Percentiles
Divide data into 100 equal parts (P1-P99)
Range Formula
Maximum - Minimum
Interquartile Range (IQR) Formula
Q3 - Q1
Mean Absolute Deviation (MAD)
Average absolute differences from the mean
Variance
Average squared difference from the mean
Population Variance Formula
σ2
Simple Variance Formula
s2
Standard Deviation (SD) Formula
√σ2
Coefficient of Variation (CV)
σ/x x 100
Z-Score Formula
x - mean / SD
Skewness
Describes asymmetry in data distribution
Negative Skew
Tail on the left
mean < median
Zero Skew
Symmetric distribution
mean = median = mode
Positive Skew
Tail on the right
mean > median
Kurtosis
Describes the peakness of a distribution
Leptokurtic
High peak, heavy tails
Mesokurtic
Normal peak (K = 3)
Platykurtic
Flat peal, light tails