## Learning Math: Data Analysis, Statistics, and Probability

# Random Sampling and Estimation

## Learn how to select a random sample and use it to estimate characteristics of an entire population. Learn how to describe variation in estimates, and the effect of sample size on an estimate's accuracy.

**In This Session**

Part A:Random Samples

Part A:

**Selecting the Sample**

Part B:

Part B:

**Investigating Variation in Estimates**

Part C:

Part C:

**The Effect of Sample Size**

Part D:

Part D:

Homework

Homework

In this session, you will learn how to use results from a random sample to estimate characteristics of an entire population. To predict the accuracy of your estimates, you will investigate the variation in estimates based on repeated random samples from that population. See Note 1 below.

**Learning Objectives
**In this session, you will estimate population quantities from a random sample. You will learn how to do the following:

• Define an estimate based on sample data

• Select a random sample

• Describe sample-to-sample variation

• Predict the accuracy of an estimate

• Assess the effect of sample size on the accuracy of an estimate

### Key Terms

**Previously Introduced:**

box plot

distribution

interval

population

random assignment

sample

stem and leaf plot

**New in This Session:**

sample mean

sample size

sampling with replacement

sampling without replacement

### Notes

**Note 1
**This session considers the use of random sampling for estimating characteristics of an entire population. Random sampling leads to random variation in estimates, and this variation can be described by a probability distribution. The normal curve approximation, which some statistics learners may be familiar with, is described only briefly. A stem and leaf plot of typical results of independent sample estimates is used for the investigations, which removes a level of abstraction from the description of sampling concepts.