Descriptive Statistics

Central Tendency

Measures of central tendency include:

Arithmetic Mean: Sum of values divided by count.

Median: 0.5 quantile (middle value).

Mode: Most frequent value.

Geometric Mean: nth root of the product of n values.

Harmonic Mean: Reciprocal of the arithmetic mean of reciprocals.

Trimmed Mean: Arithmetic mean after removing a percentage of extreme values.

【Excel】

Example file: Samples\ch21\Excel Functions\Descriptive Statistics - Central Tendency.xlsx.

Mean: =AVERAGE(A2:A85) → 143.7738

Median: =MEDIAN(A2:A85) → 143.5

Mode: =MODE(A2:A85) → 142

Geometric Mean: =GEOMEAN(A2:A85) → 143.6506

Harmonic Mean: =HARMEAN(A2:A85) → 143.5264

Trimmed Mean: =TRIMMEAN(A2:A85) → 143.8

【Python pandas】

Use mean() (mean), median() (median), and mode() (mode) for Series objects.

Dispersion

Measures of dispersion include:

Range: Max - Min.

Variance: Average of squared differences from the Mean.

Mean Absolute Deviation (MAD): Average of absolute differences from the Mean.

Standard Deviation: Square root of variance.

Interquartile Range (IQR): 0.75 quantile - 0.25 quantile.

【Excel】

Example file: Samples\ch21\Excel Functions\Descriptive Statistics - Dispersion.xlsx.

Range: =MAX(A2:A85)-MIN(A2:A85) → 32

Variance: =VAR(A2:A85) → 35.64702

MAD: =AVEDEV(A2:A85) → 4.630952

Std: =STDEV(A2:A85) → 5.970512

IQR: =PERCENTILE.EXC(A2:A85,0.75)-PERCENTILE.EXC(A2:A85,0.25) → 8

【Python pandas】

Use max(), min() (range), var() (variance), std() (std), mad() (MAD), and quantile() (quantiles).