7.SP.1
2012
Domain: Statistics and Probability
Cluster: Use random sampling to draw inferences about a population
Standards:7.SP.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 the
population. Understand the random sampling tends to produce representative samples and support valid inferences
Essential Questions

How can you use
sampling to gain
information about a
population?
Content Statements
Student will be able to:
 Compare and analyze
sampling methods.

Use a sampling method,
collect data, and
summarize results.

Determine whether or
not a survey is biased or
not
Assessments
Enduring Understandings
Students will understand that:
 Ability to describe and
identify population, sample
of a population, random
sampling, validity, reliability,
invalid, inferences.
Activities, Investigation, and Student Experiences
Activity:
 Have students work in groups to develop a way to survey
a random sample of students from the whole school.
Have groups share their plans and vote on the best one.
Then develop a questionnaire as a class and carry out the
plan.
Student Experiences:
 Abby is planning a big birthday party. She has invited
everyone in her grade and has sent 80 invitations.
Unfortunately, she forgot to include an RSVP on the
invitation, and she wants to know how many people are
coming to the party. On the invitation, Abby requested
no gifts. Instead she is asking everyone to make a
donation to her favorite charity. How much money can
Abby make for her charity at her birthday party?
Use a Sample to Make a Prediction:
 Abby asked 10 of her closest friends, and 9 of them will
be attending the party.
 Based on this survey, how many people should Abby
expect to come to the party?
 Who is the population in this event?
7.SP.1

A manager of XQJ Software surveyed 200 company
employees to find out how many of the employees
walk to work. The results are shown in the table. Do
you think the manger chose a random sample? Why
or why not?
Employees at XQJ Software
Total Number
# Who Walk
Population
9,200
300
Sample
200
40

The school food service wants to increase the number
of students who eat hot lunch in the cafeteria. The
student council has been asked to conduct a survey of
the student body to determine the students’
preferences for hot lunch. They have determined two
ways to do the survey. The three methods are listed
below. Determine if each survey option would
produce a random sample.


Comparing Populations:
The first 10 monetary donations from boys and the first 10
monetary donations from girls were recorded.
Boys Donations
15,10,10,5,12,20,15,5,10,10
2. Survey the first 20 students that enter the
lunchroom.
Which survey option should the student
council use and why?
Who is the sample in Abby’s survey?
Is the sample random? Explain?
Using a Random Sample to Make a Prediction:
 Why is it important for a sample to be random in order to
make an accurate prediction?
 How might Abby obtain a random sample?
 Abby has a list of everyone in her class, She numbers all
the names in the list from 1 to 80 Then, Abby uses her
graphing calculator to generate 20 random numbers. She
emails each of the people who correspond to the
randomly generated numbers and asks whether or not he
or she plans to attend the party. Of the 20 people
surveyed, 6 are not able to come to the party. Based on
this sample, predict the total number people who will
attend the party.
1. Write all of the students’ names on cards
and pull them out in a draw to determine who
will complete the survey.
3. Survey every 3rd student who gets off a
bus.
2012
Girls Donations
10,20,5,1,20,25,15,15,10,5



Make a dot plot for each set of data.
What can you infer about the donations of each of the
populations?
Find the mean and the mean deviation for the boys’ and
7.SP.1
2012
girls’ donations.
Equipment Needed:

Interactive Whiteboards

Board Approved Textbooks

Overhead Projector

Graphing Calculators
Answer the question:
 To find the average student donation, average the girls’
mean donation and the boys’ mean donation.
 Based on the mean student donation and Abby’s
prediction form how many people will come to her party,
how much money could be raised in donations?
Teacher Resources:
Illustrative Mathematics Project
 Illustrations
NCTM Illuminations
 About Our Class
 Capture – Recapture
 How Much is a Million?
Online Practice from IXL
 Statistics: Identify representative, random, and biased
samples