Basic Descriptive Statistics with NumPy

NumPy provides efficient functions for arrays of numbers:

%%%python import numpy as np

Porosity measurements from 10 core plugs (%)

porosity = np.array([12.1, 15.3, 14.8, 18.2, 11.5, 16.7, 13.9, 19.0, 15.1, 14.4])

mean_val = np.mean(porosity) # 15.1 median_val = np.median(porosity) # 15.0 std_val = np.std(porosity, ddof=1) # ddof=1 for sample std var_val = np.var(porosity, ddof=1) # sample variance min_val = np.min(porosity) max_val = np.max(porosity)

print(f"Mean: {mean_val:.2f}%") print(f"Median: {median_val:.2f}%") print(f"Std: {std_val:.2f}%") print(f"Var: {var_val:.2f}") print(f"Range: {min_val:.1f} to {max_val:.1f}") %%%

Important: Use ddof=1 in np.std() and np.var() for the sample standard deviation and variance (divides by $n-1$). The default ddof=0 gives the population version (divides by $n$).

Percentiles and Quartiles

%%%python

Compute quartiles

Q1 = np.percentile(porosity, 25) Q2 = np.percentile(porosity, 50) # same as median Q3 = np.percentile(porosity, 75) IQR = Q3 - Q1

print(f"Q1 = {Q1:.2f}, Q2 = {Q2:.2f}, Q3 = {Q3:.2f}") print(f"IQR = {IQR:.2f}")

Detect outliers

lower_fence = Q1 - 1.5 * IQR upper_fence = Q3 + 1.5 * IQR outliers = porosity[(porosity < lower_fence) | (porosity > upper_fence)] print(f"Outliers: {outliers}") %%%

Pandas describe() — Quick Summary

Pandas gives a one-line summary of any DataFrame column:

%%%python import pandas as pd

Create a DataFrame from well data

df = pd.DataFrame({ "well": ["A1", "A2", "A3", "A4", "A5", "A6", "A7", "A8"], "depth_m": [1200, 1350, 1500, 1650, 1800, 1950, 2100, 2250], "porosity": [24.1, 22.3, 19.8, 18.5, 16.2, 14.9, 13.1, 11.7], "perm_mD": [450, 320, 180, 120, 75, 45, 25, 12] })

Quick statistical summary

print(df.describe())

Shows count, mean, std, min, 25%, 50%, 75%, max for each numeric column

Summary for a single column

print(df["porosity"].describe()) %%%

Histograms with Matplotlib

Histograms show the distribution shape of your data:

%%%python import matplotlib.pyplot as plt

Histogram of porosity values

plt.figure(figsize=(8, 5)) plt.hist(df["porosity"], bins=6, color="steelblue", edgecolor="black", alpha=0.7) plt.xlabel("Porosity (%)") plt.ylabel("Frequency") plt.title("Porosity Distribution — Well Data") plt.axvline(df["porosity"].mean(), color="red", linestyle="--", label=f'Mean = {df["porosity"].mean():.1f}%') plt.legend() plt.tight_layout() plt.show() %%%

Box Plots for Comparing Groups

%%%python

Compare porosity distributions from two formations

formation_A = [22.1, 24.5, 19.8, 23.2, 21.0, 25.3, 20.1] formation_B = [14.5, 16.2, 12.8, 15.9, 13.4, 17.1, 14.0]

plt.figure(figsize=(6, 5)) plt.boxplot([formation_A, formation_B], labels=["Formation A", "Formation B"]) plt.ylabel("Porosity (%)") plt.title("Porosity Comparison by Formation") plt.grid(axis="y", alpha=0.3) plt.tight_layout() plt.show() %%%

The box shows $Q_1$ to $Q_3$, the line inside is the median, and the whiskers extend to the farthest non-outlier points.

Hypothesis Testing with SciPy

%%%python from scipy import stats

One-sample t-test: is the mean porosity = 20%?

t_stat, p_value = stats.ttest_1samp(df["porosity"], 20.0) print(f"t-statistic: {t_stat:.3f}") print(f"p-value: {p_value:.4f}") if p_value < 0.05: print("Reject H0: mean porosity is significantly different from 20%") else: print("Fail to reject H0: not enough evidence to say mean differs from 20%")

Two-sample t-test: compare Formation A vs Formation B

t_stat2, p_value2 = stats.ttest_ind(formation_A, formation_B) print(f"\nTwo-sample t-test: t = {t_stat2:.3f}, p = {p_value2:.4f}") %%%

Correlation Matrix

%%%python

Compute and display correlation matrix

corr_matrix = df[["depth_m", "porosity", "perm_mD"]].corr() print(corr_matrix)

Scatter plot with correlation

plt.figure(figsize=(6, 5)) plt.scatter(df["depth_m"], df["porosity"], color="teal", s=60) plt.xlabel("Depth (m)") plt.ylabel("Porosity (%)") plt.title(f'Depth vs Porosity (r = {df["depth_m"].corr(df["porosity"]):.3f})') plt.tight_layout() plt.show() %%%