Statistics, Sampling Methods, and Data Analysis Techniques

Simple random sampling

Every item has equal chance of selection

Stratified sampling

Population divided into groups (strata) and all groups represented

Cluster sampling

Select a few groups (clusters) instead of entire population

Convenience sampling

Sample chosen based on ease, not randomness

Mean

Average = sum ÷ n

Median

Middle value of ordered data

Mode

Most frequent value

Descriptive statistics

Measures that summarize data (mean, median, etc.)

Range

Maximum minus minimum

Variance

Average squared deviation from the mean

Standard deviation

Square root of variance

Null hypothesis (H0)

Base case, no relationship

Alternative hypothesis (Ha)

What we believe or test for

Significance level (alpha)

Threshold to reject H0

p-value

Probability of results if H0 is true

Reject H0

p-value is less than or equal to alpha

Fail to reject H0

p-value is greater than alpha

t-test

Compares means of two groups

Paired t-test

Compares related groups (before and after)

ANOVA

Compares means of three or more groups

Chi-square test

Tests categorical data vs expected distribution

Correlation

Measures relationship between two variables

Correlation = 1

Perfect positive relationship

Correlation = -1

Perfect negative relationship

Correlation = 0

No relationship

Regression

Predicts dependent variable using independent variable(s)

Dependent variable (y)

Output being predicted

Independent variable (x)

Input used to predict

Slope (m)

Rate of change

Intercept (b)

Starting point on y-axis

Descriptive analytics

Answers 'What happened?' or 'What is happening?' by summarizing and organizing data using statistics like mean, median, totals, and reports to understand past performance

Diagnostic analytics

Answers 'Why did it happen?' by analyzing data to find causes, relationships, patterns, anomalies, and outliers using drill-down analysis and statistical techniques

Predictive analytics

Answers 'What will happen?' by using historical data, trends, probability, and models (like regression) to forecast future outcomes and estimate likelihoods

Prescriptive analytics

Answers 'What should we do?' by recommending actions based on predictions and constraints to optimize decisions, improve performance, and achieve the best outcome

Adaptive analytics

Learns and improves using data and AI over time

Exploratory data analytics

Initial analysis to explore and summarize data

Purpose of EDA

Find patterns, anomalies, and generate questions

HRMS

Manages employee data

CRM

Manages customer interactions

SCM

Tracks supply chain processes

FRS

Financial reporting system

Horizontal analysis

Compares changes over time

Vertical analysis

Compares items as a percentage of a base value

Diagnostic analytics (technique)

Explains why something happened using deeper analysis

Anomaly

Data point outside expected pattern

Outlier

Extreme value in dataset

Drill-down analysis

Breaks data into deeper levels to find causes

Benford's Law

First digits follow predictable distribution

Purpose of Benford's Law

Detect fraud or anomalies in data