Statistics for Data Analysts — Practical Guide India 2026

What Statistics Does a Data Analyst Actually Need?

Statistics textbooks cover enormous ground — much of it irrelevant to an analyst's daily work. This chapter covers only the statistics that appear in real analysis tasks and job interviews in India. Think of this as applied statistics, not academic statistics.

1. Descriptive Statistics — Summarising What You See

Descriptive statistics turn a column of numbers into a story. Before any analysis, every analyst should run describe() and know what each number means in business terms.

import pandas as pd
import numpy as np

df = pd.read_csv('orders.csv')

# The first thing you should always run
print(df['order_value'].describe())
# Output:
# count    10000.000
# mean      1842.50      <-- average order value
# std       2310.00      <-- high std = wide spread = outliers likely
# min         50.00
# 25%        450.00      <-- 25% of orders are below ₹450
# 50%        980.00      <-- median — half above, half below ₹980
# 75%       2100.00      <-- 75% of orders are below ₹2,100
# max      85000.00      <-- one massive outlier pulling mean up

# Mean vs median gap: ₹1842 vs ₹980 → strong right skew → use median
print(f"Skewness: {df['order_value'].skew():.2f}")  # > 1 = right-skewed

# Percentile check
for p in [90, 95, 99]:
    print(f"P{p}: ₹{df['order_value'].quantile(p/100):,.0f}")

2. Probability Distributions — Four You Must Recognise

You do not need to derive these distributions mathematically. You need to recognise which distribution describes your data and what that implies for your analysis.

from scipy import stats
stat, p = stats.shapiro(df['column'])
print('Normal' if p > 0.05 else 'Not normal')

# Visualise
df['order_value'].hist(bins=50)
# If right tail is long → right-skewed → prefer log transform

from scipy.stats import binom
# P(exactly k conversions out of n visits with rate p)
binom.pmf(k=50, n=1000, p=0.04)

from scipy.stats import poisson
# P(exactly k events given avg rate lambda)
poisson.pmf(k=5, mu=3.2)  # 3.2 tickets/hour avg

3. Hypothesis Testing — The Framework

Hypothesis testing answers a specific question: is the difference we observed in the data real, or could it have happened by random chance? Every A/B test, every "our conversion rate went up this month" claim, and every "product A sells better than product B" conclusion should go through this framework.

Which Test to Use

from scipy import stats
import numpy as np

# Two-sample t-test: Mumbai vs Delhi order values
mumbai_orders = df[df['city'] == 'Mumbai']['order_value']
delhi_orders  = df[df['city'] == 'Delhi']['order_value']

t_stat, p_value = stats.ttest_ind(mumbai_orders, delhi_orders)
print(f"t-statistic: {t_stat:.3f}")
print(f"p-value: {p_value:.4f}")
print(f"Conclusion: {'Significant difference' if p_value < 0.05 else 'No significant difference'} at α=0.05")

# z-test for proportions: A/B test on conversion rate
from statsmodels.stats.proportion import proportions_ztest

conversions = [45, 62]      # A: 45 converted, B: 62 converted
nobs        = [1000, 1000]  # 1000 visitors each

z_stat, p_val = proportions_ztest(conversions, nobs)
print(f"z-stat: {z_stat:.3f}, p-value: {p_val:.4f}")
print(f"CVR A: {45/1000:.2%}, CVR B: {62/1000:.2%}")
if p_val < 0.05:
    print("Variant B wins — roll out to all users")
else:
    print("Difference not statistically significant — do not call a winner yet")

4. A/B Testing — Practical Walkthrough

A/B testing is hypothesis testing applied to product or marketing decisions. It is one of the most common analyst responsibilities at startups, e-commerce companies, and product teams — and one of the most commonly misused.

# Step 1: Calculate required sample size BEFORE starting
from statsmodels.stats.power import NormalIndPower

analysis = NormalIndPower()
n = analysis.solve_power(
    effect_size=0.2,   # minimum detectable effect (Cohen's d)
    alpha=0.05,        # significance level
    power=0.80,        # 80% chance of detecting a real effect
    alternative='two-sided'
)
print(f"Required sample size per group: {int(n)}")
# → ~197 per group. Run until you have 197 in EACH group.

# Step 2: After test ends, analyse results
from scipy.stats import ttest_ind

control   = df[df['variant'] == 'A']['revenue_per_session']
treatment = df[df['variant'] == 'B']['revenue_per_session']

t, p = ttest_ind(control, treatment)
lift = (treatment.mean() - control.mean()) / control.mean()

print(f"Control mean:   ₹{control.mean():.2f}")
print(f"Treatment mean: ₹{treatment.mean():.2f}")
print(f"Relative lift:  {lift:.1%}")
print(f"p-value:        {p:.4f}")
print(f"Statistically significant: {p < 0.05}")

5. Correlation — Measuring Relationships in Data

Correlation quantifies how strongly two variables move together. It ranges from -1 (perfect negative — when one goes up, the other goes down) to +1 (perfect positive — they move together exactly). Zero means no linear relationship.

import seaborn as sns
import matplotlib.pyplot as plt

# Correlation matrix for numeric columns
corr = df[['revenue', 'visits', 'avg_session_time', 'cart_adds']].corr()

# Heatmap
plt.figure(figsize=(8, 6))
sns.heatmap(corr, annot=True, fmt='.2f', cmap='coolwarm',
            vmin=-1, vmax=1, center=0)
plt.title('Correlation Matrix — Sales Metrics')
plt.tight_layout()
plt.savefig('correlation_heatmap.png')

# Pearson r between two specific columns
from scipy.stats import pearsonr
r, p = pearsonr(df['ad_spend'], df['revenue'])
print(f"Correlation: {r:.3f}, p-value: {p:.4f}")
# r=0.72, p<0.05 → strong positive correlation, statistically significant

6. Linear Regression — Prediction and Driver Analysis

Linear regression fits a line through data to quantify the relationship between a dependent variable (what you want to predict) and one or more independent variables (the drivers). For data analysts, the most useful output is the coefficients — they tell you how much the outcome changes per unit change in each driver.

import statsmodels.api as sm
import pandas as pd

# Business question: what drives monthly revenue?
# Independent variables (drivers): ad_spend, num_products, avg_price, month_num
X = df[['ad_spend', 'num_products', 'avg_price', 'month_num']]
y = df['monthly_revenue']

# Add constant (intercept)
X = sm.add_constant(X)

# Fit the model
model = sm.OLS(y, X).fit()
print(model.summary())

# Key outputs to read:
# R-squared: how much variance in revenue is explained (e.g., 0.82 = 82%)
# Coefficients: for every ₹1 increase in ad_spend, revenue increases by ₹coef[ad_spend]
# p-values: is each coefficient statistically significant? (p < 0.05 = yes)

# Simpler version with sklearn
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score

model_sk = LinearRegression()
model_sk.fit(X_train, y_train)
y_pred = model_sk.predict(X_test)
print(f"R² on test set: {r2_score(y_test, y_pred):.3f}")

# Coefficients
for feature, coef in zip(X_train.columns, model_sk.coef_):
    print(f"{feature}: ₹{coef:.2f} per unit increase")

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