# Make Inferences from Samples

Video lessons with examples and solutions to help Grade 7 students understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Common Core: 7.SP.2

### Suggested Learning Targets

• I can draw inferences from a random data sample from a table or graph.
• I can draw inferences from a random data sample without a table or graph.
• I can collect and use multiple samples of data to make generalizations about population.
• I can generate multiple samples of the same size to gauge the variations in estimates or predictions.

Vocabulary

population:  The entire set of items from which data can be selected.

sample:
A selection from a population.

representative sample:
A sample that is similar to the entire population

random sample:
A sample chosen at random; A sample chosen from a population such that each data unit in the population has an equal chance of being chosen each time

systematic sample: A sample chosen according to a rule or formula (Example:  Survey every 10th person through the door.)

convenience sample: A sample that is easiest to reach (Example: Survey the first 10 people through the door.)

voluntary-response sample: Members volunteer to be in the sample.

Making Inferences from Data
This Video discusses how to make inferences from a valid survey using proportional reasoning.
Example 1: You are going to produce tennis shoes that come in 3 different colors. In order to decide how many to make in each color you conduct a survey. Of the 300 people you survey, 75 said that they would purchase the yellow shoes. If you are going to make 10,000 pairs of shoes, how many should be yellow.
Example 2: In order to measure Monarch butterfly migration, scientist tag and release 100 butterflies in Kansas and Missouri before traveling to Mexico a few weeks later. While in Mexico, the same scientist captured another 100 butterflies of which 15 are tagged. Based on this information, how many butterflies would you predict start in Kansas and Missouri and migrate to Mexico?

Errata in the video: 75 x 10,000 = 750,000, x = 2,500 yellow shoes.

Activity 1:

Below is the data collected from two random samples of 100 students regarding student's school lunch preference.
Make at least two inferences based on the results.

 Student Tacos Hamburgers Pizza Total # 1 12 14 74 100 #2 12 11 77 100

Solution:
• Most students prefer pizza.
• More people prefer pizza and hamburgers and tacos combined.

Activity 2:

Given the first name of all students in your grade. Predict the most common name in the U.S. for 7th graders. How good an estimate do you think your sample provides? Explain your reasoning.

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