BIOSTATS - Descriptive Statistics

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