Probability & Statistics for Data Analytics

1. Introduction

Statistics helps analysts separate stable patterns from variation in observed data. Probability describes uncertainty about outcomes; statistical methods use samples to reason about a broader process while acknowledging that a result can be uncertain.

2. Core concepts

A population is the full group of interest and a sample is the observed subset. Mean is sensitive to extreme values; median is often more robust for skewed distributions. A confidence interval describes a procedure’s uncertainty, not the probability that one fixed parameter changes after seeing the interval.

3. Topics covered in this module

• Population, sample, variable, bias, randomization, and sampling error
• Mean, median, variance, standard deviation, percentiles, and outliers
• Probability rules, conditional probability, Bayes reasoning, and independence
• Hypotheses, effect size, confidence intervals, p-values, and A/B testing caveats

4. Syntax and how to read it

from statistics import mean, median

values = [12, 13, 14, 15, 90]
print(mean(values), median(values))

The mean is pulled upward by the extreme value 90, while the median describes the center of this ordered sample more robustly.

5. Practical workflow

Inspect a distribution before selecting a summary, define the target population and sampling process, and report an effect size with uncertainty. Check whether groups were measured consistently and whether assignment was randomized.

6. Common mistakes

• Treating a small p-value as a measure of practical importance or proof of causality.
• Ignoring selection bias, missing outcomes, repeated testing, or changing definitions.

7. Best practices

• Show sample size, effect size, uncertainty, and relevant population limits.
• Predefine experiment outcomes and decision rules when possible.

8. Practice task

A dataset has values 1, 2, 2, 3, and 100. Which is more representative of a typical observation: mean or median, and why?

9. One possible solution

The median is 2. The extreme value 100 pulls the mean upward, so the median better describes a typical observation for this skewed sample.

10. Summary

Describe samples, distributions, uncertainty, experiments, and practical statistical comparisons. Show sample size, effect size, uncertainty, and relevant population limits. Predefine experiment outcomes and decision rules when possible.

11. What comes next

The next module, Data Visualization using Power BI, builds on this foundation and applies it to a new part of the analytics workflow.