Topics
9. Statistics
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United States of America
Grade 7

9.02 Use sample data

Lesson
Practice

Introduction

We have learned different sampling techniques in order to obtain samples. We'll now look at how to examine those samples to gain more information about the given population.

Use sample data

By examining and using statistics on samples of a population, we can extract information about that population. The information that we can get from sample data may be helpful for answering questions and making informed decisions.

We can also use data from a sample to draw inferences about a population. This means that we can generate conclusions about a population based on a sample or subset of the data.

Examples

Example 1

A random sample of 70 students were asked "What is your favorite sport?". The results are recorded in the table below:

YogaMartial ArtsHIITCyclingOther
Number of students101481523
a

Using the sample data, which exercise can we infer is liked the least by the students?

Worked Solution
Create a strategy

We will look to the data table to make our inferences. The sport with the least number of responses is the least liked sport for our sample.

Apply the idea

From the data table, we can see that HIIT has the least amount of responses. Therefore, we can infer that HIIT is the liked the least by the students.

b

If there are 315 students at the school, about how many would you expect to have yoga as their favorite exercise?

Worked Solution
Create a strategy

To estimate the number of students that will like yoga out of 315 respondents, we use the idea that the proportion of students who like yoga from 70 students is the same as the proportion that will like yoga from 315 respondents.

Apply the idea

Since 10 out of 70 students choose yoga as their favorite sport:

\displaystyle \dfrac{10}{70}\displaystyle =\displaystyle \dfrac{1}{7}Simplified ratio

To find the proportion of the number of students, 315:

\displaystyle \dfrac{1}{7}\times 315\displaystyle =\displaystyle 45Evaluate

We would expect 45 students' favorite sport to be yoga out of 315 students.

Idea summary

We can use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

Outcomes

7.SP.A.1

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

7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

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