Ch.02 Mini Project 02 — Location & Dispersion Statistics Explorer

Concept: All Ch.2 univariate statistics — location (central tendency) and dispersion — implemented from scratch using only the Python standard library.

What it does

For every numeric column in a CSV (or the built-in demo), statistics_explorer.py:

1. Location statistics — Min, Max, Mean, Mode, Median, Q1, Q2, Q3
2. Dispersion statistics — Amplitude, IQR, MAD, Standard Deviation, Variance
3. Skewness — computed and classified (symmetric / positive / negative)
4. ASCII box plot — visual five-number summary (min, Q1, median, Q3, max)
5. Central tendency check — compares mean vs. median to confirm skew direction

Usage

# Built-in demo (Weight, Height, Max_temp from the Ch.2 Friends dataset)
python statistics_explorer.py

# All numeric columns from a CSV
python statistics_explorer.py my_data.csv

No external dependencies — pure Python 3 standard library only.

Sample Output

======================================================================
  STATISTICS REPORT: Weight
  n = 14  |  Missing = 0
======================================================================

  LOCATION STATISTICS
--------------------------------------------------
  Min                       55.0000
  Max                      115.0000
  Mean (x-bar)              79.0000
  Mode                      75.0  (freq=2)
  Median (Q2)               75.0000
  Q1 (25th pct)             66.0000
  Q3 (75th pct)             85.0000

  DISPERSION STATISTICS
--------------------------------------------------
  Amplitude (max-min)       60.0000
  IQR (Q3-Q1)               19.0000
  MAD (sample)              14.3077
  Std Dev (sample)          17.3848
  Variance (sample)        302.0769

  SHAPE
--------------------------------------------------
  Skewness                  +0.8812
                            Positive (right) skew

  Box plot: Weight
  |-----------[======|=======]-----------|

Formulas Implemented

Statistic	Formula used	Notes
Mean	Σxᵢ / n	Arithmetic mean
Median	Middle value (sorted)	Exact lecture formula
Quartiles	Position method n×(k/4)	Exact lecture method
MAD	Σ|xᵢ − x̄| / (n−1)	Sample formula
Std Dev	√(Σ(xᵢ−x̄)² / (n−1))	Bessel's correction (n−1)
Skewness	Σ(xᵢ−x̄)³/n / s³	Fisher's moment coefficient

Key Concepts from Ch.2 Applied

Concept	Where it appears
Central tendency statistics	compute_mean/median/mode()
Quartile position method	compute_quartile()
Bessel's correction (n−1)	compute_std(), compute_mad()
Skewness taxonomy	classify_skewness()
Five-number summary	ascii_boxplot()

Limitations & Future Ideas

• Extension: add a --population flag to switch to population formulas (÷n instead of ÷n−1).
• Extension: add percentile computation for arbitrary quantiles.
• Extension: add the coefficient of variation (std/mean × 100%) as a relative dispersion measure.