Stats Midterm Survival Kit: Descriptive to Inferential

Most students fail statistics not because they can't do the math, but because they treat it like a math class instead of a logic class. This guide focuses on the 'why' behind the formulas.

Before you dive into the practice exam, remember: The data is trying to tell a story. Your job is to make sure you aren't misinterpreting the plot.

Statistical Domains

1. Describing Data (Without Lying) #

The goal of descriptive stats is to reduce a massive dataset into a digestible summary. But every summary loses information.

The Variance Trap: Why do we divide by n1n-1 for samples but NN for populations? It's called Bessel's Correction. Using nn would consistently underestimate the true population variance.

  • Sample Variance:s2=(xixˉ)2n1s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}
  • Standard Deviation:s=s2s = \sqrt{s^2}
Info

Pro Tip: If your distribution is skewed, the Mean is a liar. Use the Median and IQR (Interquartile Range) to describe 'typical' values in datasets with heavy outliers (like house prices or salaries).

Skewed Salary Data
category
salary
Entry Level
45000
Mid Level
75000
Senior
110000
Executive
450000
Select a Data component to power this chart

Essential Reference Table #

Goal
Tool/Test
Requirement
Compare a sample mean to a known μ\mu
One-sample Z-test
Known σ\sigma, n>30n > 30
Compare two group means
Independent T-test
Unknown σ\sigma, equal variance
Predict a value (yy) from (xx)
Simple Linear Regression
Linear relationship, homoscedasticity
Test relationship between categories
Chi-Square Test
Categorical data (counts)
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