Unit 8, Lesson 9
What Makes a Good Sample?
Accelerated 6
Preparation
Lesson Narrative
In this lesson, students examine multiple samples from the same population and learn what it means for a sample to be representative of the population. A sample is representative of a population if its distribution resembles the population's distribution in center, shape, and spread. Students look at the structure of dot plots, attending to center, shape, and spread, to help them compare the samples and the population (MP7). Although earlier activities pointed out the usefulness of using samples when working with large populations, the problems in this lesson use smaller populations so that students can compare each sample against the entire population.
An optional activity is included as extra practice for students to understand the relationship between a sample and population.
- Calculate the mean or median of various samples, and compare them with the mean or median of the population.
- Comprehend that the term “representative” (in spoken and written language) refers to a sample with a distribution that closely resembles the population’s shape, center, and spread.
- Given dot plots, determine whether a sample is representative of the population, and explain (orally and in writing) the reasoning.
Let’s see what makes a good sample.
Required Materials
Activity 2
Required Preparation
None
A sample is representative of a population if they match closely. They are very alike in shape, center, and spread.
This dot plot shows the distribution for a population.
A dot plot labeled dollars per pound of catfish. The numbers 1.6 through 2.8 in increments of zero point 2 are indicated. The data are as follows: 1 point 6 dollars per pound, 4 dots. 1 point 7 dollars per pound, 20 dots. 1 point 8 dollars per pound, 24 dots. 1 point 9 dollars per pound, 2 dots. 2 dollars per pound, 10 dots. 2 point 1 dollars per pound, 2 dots. 2 point 2 dollars per pound, 6 dots. 2 point 3 dollars per pound, 4 dots. 2 point 4 dollars per pound, 4 dots. 2 point 5 dollars per pound, 6 dots. 2 point 6 dollars per pound, 10 dots. 2 point 7 dollars per pound, 4 dots. 2 point 8 dollars per pound, 4 dots.
This dot plot shows the distribution of a sample that is representative of the population.
A dot plot labeled dollars per pound of catfish. The numbers 1.6 through 2.8 in increments of zero point 2 are indicated. The data, titled Sample 1, are as follows: 1 point 6 dollars per pound, 1 dots. 1 point 7 dollars per pound, 4 dots. 1 point 8 dollars per pound, 5 dots. 2 dollars per pound, 2 dots. 2 point 2 dollars per pound, 2 dots. 2 point 4 dollars per pound, 1 dot. 2 point 5 dollars per pound, 2 dots. 2 point 6 dollars per pound, 2 dots. 2 point 7 dollars per pound, 1 dot. 2 point 8 dollars per pound, 1 dot