Lesson 1: From Sample to Population

From Sample to Population

In Statistics 1, we focused on Descriptive Statistics—summarizing and describing the data we have. Now, in Statistics 2, we move to Inferential Statistics.

The Big Question

How can we draw conclusions about a massive Population when we only have a small Sample?

Key Concepts

1. Population vs. Sample

Population ( $N$ ): The entire group we are interested in (e.g., all voters in a country).
Sample ( $n$ ): A subset of the population that we actually collect data from (e.g., 1000 surveyed voters).

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2. Parameter vs. Statistic

Parameter: A numerical characteristic of the population (e.g., Population Mean $\mu$ ). This is usually unknown.
Statistic: A numerical characteristic of the sample (e.g., Sample Mean $\bar{x}$ ). This is calculated from data.

Goal of Inference:

We use the Statistic (which we know) to estimate the Parameter (which we don’t know).

$\bar{x} \approx \mu$

The Magic: Central Limit Theorem (CLT)

The CLT states that if you take sufficiently large random samples from a population (with any distribution), the distribution of the sample means will be approximately Normally Distributed.

This is powerful because it allows us to use the properties of the Normal Distribution to make probability statements about our estimates.

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Lesson 1