Statistics for Data Analytics

Why Statistics for Analysts?

Statistics helps you: ✅ Summarize large datasets ✅ Identify patterns and outliers ✅ Test hypotheses ✅ Quantify uncertainty ✅ Make data-backed predictions

Descriptive Statistics

Measures of Central Tendency

Mean (Average):

Mean = Sum of all values / Count
Example: [10, 20, 30] → Mean = 20

Median (Middle Value):

Sort data, pick middle value
Example: [10, 15, 100] → Median = 15
(Better than mean when outliers exist!)

Mode (Most Frequent):

Example: [1, 2, 2, 3] → Mode = 2

Measures of Spread

Range:

Range = Max - Min
Example: [10, 50] → Range = 40

Variance: Average of squared differences from mean

High variance = Data is spread out
Low variance = Data is clustered

Standard Deviation (σ): Square root of variance

±1σ contains ~68% of data
±2σ contains ~95% of data
±3σ contains ~99.7% of data

Probability Basics

Probability = Favorable outcomes / Total outcomes

Example: Probability of rolling 6 on dice = 1/6 = 16.7%

Key Concepts

Independent events: Coin flip outcomes don't affect each other
Dependent events: Drawing cards without replacement
Conditional probability: P(A|B) = Probability of A given B happened

Correlation vs Causation

Correlation

Measures relationship strength between two variables (-1 to +1).

+1 = Perfect positive (both increase together)
0 = No relationship
-1 = Perfect negative (one increases, other decreases)

Example: Ice cream sales correlate with drowning deaths (both increase in summer), but ice cream doesn't cause drowning!

Causation

One variable directly causes change in another.

Establish causation:

Correlation exists
Temporal order (cause before effect)
No confounding variables
Controlled experiment

Normal Distribution (Bell Curve)

Most data in nature follows a bell curve.

Properties:

Mean = Median = Mode (center)
Symmetric
68-95-99.7 rule applies

Real examples:

Heights
Test scores
Measurement errors

Hypothesis Testing

The Process

State hypothesis
- H0 (Null): No effect
- H1 (Alternative): There is an effect
Collect data
Calculate p-value
- Probability of seeing results if H0 is true
Decide
- p < 0.05: Reject H0 (statistically significant!)
- p ≥ 0.05: Fail to reject H0

Example

Question: Did new website design increase sales?

H0: New design has no effect
H1: New design increases sales

Results: p-value = 0.02

Conclusion: Reject H0. Design likely increased sales (95% confidence).

Confidence Intervals

Range where true value likely lies.

Example: "Average customer age is 35 ± 2 years (95% CI)" = We're 95% confident true average is between 33-37.

Statistical Significance

p-value < 0.05 = Statistically significant

What it means:

Less than 5% chance result is due to random chance
NOT the same as "important" or "large effect"

Example:

Finding: Website tweak increases clicks by 0.1%
p-value: 0.001 (highly significant!)
But: 0.1% increase might not be business-relevant

Common Distributions

| Distribution | Use Case | |--------------|----------| | Normal | Heights, test scores | | Binomial | Success/failure (coin flips) | | Poisson | Event counts (website visits/hour) | | Uniform | Random number generators |

Real Example: Salary Analysis

Dataset: 1000 employee salaries

Questions to answer:

What's typical salary?
- Mean: ₹52,000
- Median: ₹48,000 (better - not affected by CEO's ₹5M salary!)
How spread out are salaries?
- Standard deviation: ₹15,000
- 68% of employees earn ₹37K-₹67K
Are salaries normally distributed?
- Check histogram - if bell-shaped, yes
Do engineers earn more than designers?
- Hypothesis test
- p-value = 0.03
- Yes, statistically significant difference!

Python for Statistics

code.pyPython

import pandas as pd
import numpy as np

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

# Descriptive stats
print(df['revenue'].mean())
print(df['revenue'].median())
print(df['revenue'].std())

# Correlation
correlation = df['ad_spend'].corr(df['revenue'])
print(f"Correlation: {correlation}")

# Hypothesis test (t-test)
from scipy import stats
group_a = df[df['variant']=='A']['conversion_rate']
group_b = df[df['variant']=='B']['conversion_rate']
t_stat, p_value = stats.ttest_ind(group_a, group_b)
print(f"p-value: {p_value}")

Common Mistakes

❌ Confusing correlation with causation ✅ Remember: Correlation ≠ Causation

❌ p-hacking (testing until you get p<0.05) ✅ Define hypothesis before collecting data

❌ Ignoring sample size ✅ Larger samples = more reliable results

❌ Assuming significance = importance ✅ Consider practical significance too

Summary

✅ Mean vs Median (use median for outliers) ✅ Standard deviation measures spread ✅ Correlation ≠ Causation ✅ p < 0.05 = Statistically significant ✅ Confidence intervals quantify uncertainty ✅ Hypothesis testing proves/disproves theories

Next: A/B Testing & Experimentation! 🧪