Variability Between Samples

Learn sampling variability, unbiased sample means.

Lesson 1 of 32 parts Practice Flashcards

1/2

Sampling Variability

Objective: Explain sampling variability, apply the stated method, and check its conditions.

Different random samples from the same population generally give different statistics. A sampling distribution records that variation over repeated samples using the same design and size. A difference between two sample estimates alone does not demonstrate a changed population parameter. Sampling variability is distinct from evidence of a population change.

Formulas

Sampling variation = changes in a statistic across repeated samples

Worked examples

Try itTwo synthetic samples from one population have means 13 and 7. Find the difference of sample means.Show answer

Step 1: Different random samples can produce different estimates. Step 2: Subtract 7 from 13. Step 3: The difference is 6; this alone does not prove a population changed.

Swipe sideways to move between sections

Sampling Variability

Objective: Explain sampling variability, apply the stated method, and check its conditions.

Formulas

Sampling variation = changes in a statistic across repeated samples

Worked examples

Try itTwo synthetic samples from one population have means 13 and 7. Find the difference of sample means.Show answer

Step 1: Different random samples can produce different estimates. Step 2: Subtract 7 from 13. Step 3: The difference is 6; this alone does not prove a population changed.

Unbiased Sample Means

Objective: Explain unbiased sample means, apply the stated method, and check its conditions.

For identically distributed observations with finite mean μ, E[x̄]=μ. Independence is needed for the usual simple variance formula, not for expectation linearity itself. Unbiasedness describes the center over repeated samples and does not guarantee one sample is accurate. Unbiased does not mean every estimate equals the true parameter.

Formulas

$E[x̄]=μ$

Worked examples

Try itA population has mean μ=7 and finite variance. For independent random samples of size 36, what is E[x̄]?Show answer

Step 1: The sample mean is unbiased under this design. Step 2: E[x̄]=μ, regardless of the stated sample size. Step 3: The sampling-distribution center is 7.

You finished the reading!

Lock it in with a few practice questions, then move on to the next lesson.

Practice Next lesson

Next lessonThe Central Limit Idea