STATISTICS and USING SAMPLES TO DRAW INFERENCES
Statistics can be used to gain information about a population. The population is the group
being studied. If a population is very large, it is impossible to gather data from each member of
the population. So, a sample of that population is chosen instead, and the data collected from
the sample are used to make generalizations about the larger population. For the generalization
to be reliable, however, the sample must be a representative sample. A representative sample
is similar to the population from which it was drawn. It is also important to have a large sample
to obtain information about a population.
Random samples tend to be representative. In a random sample, every member of the
population has an equal chance of being chosen. Biased samples are ones in which some
members of the population have a greater chance of being chosen than others. Because of a
bias, the sample usually does not represent the population well.
EXAMPLE 1- Random Sample
Gage wants to sample students to find out how many books they read over the summer. Which
of the following groups would be a random sample? Explain.
A. all the students in the library
B. all the students in an honors class
C. every tenth students entering a lunchroom
C is the random sample. It is the only choice where everyone in the school
_______________________________________________________________________
_______________________________________________________________________
(the population) has an equal chance of being selected.
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
EXAMPLE 2 – Biased Sample
Corbyn wants to find out what type of vehicle is most popular among
drivers in his town. To create a sample, he decides to walk around a
schools parking lot and survey people who drive SUVs as they wait to pick
up their children. Is this sample biased? If so, why and how can Corbyn
make the sample less biased?
Yes, this sample is biased. Only SUV drivers with children at the school can
_______________________________________________________________________
be selected. The population is drivers who live in the town. To make the
_______________________________________________________________________
_______________________________________________________________________
sample less biased Corbyn could… [students finish with their own ideas]
_______________________________________________________________________
_______________________________________________________________________
Directions: For questions 1 through 2, explain whether or not the solution
would provide a random sample.
1. Determining the nation’s favorite ice cream flavor by asking a group of customers in one ice
cream shop.
This is a biased sample. Not everyone in the nation (the population) has an equal
_______________________________________________________________________
chance of being chosen, only people in that one shop.
_____________________________________________________________
2. Determining how guests rate the food at a certain restaurant by asking every tenth person
who leaves the restaurant.
This is a random sample. Since the population is the guests of that restaurant,
_______________________________________________________________________
everyone in the population has a chance to be selected.
_____________________________________________________________
Directions: Use the information below for questions 3 through 4.
Gerald wants to know if most students at his middle school support buying new
football uniforms. Which survey described below would result in biased
samples? Briefly explain.
3. Survey every student in Gerald’s seventh-grade homeroom.
This is a biased sample. Not everyone in the school (the population) has an equal
_______________________________________________________________________
th
chance of being chosen, only people in that one 7 grade homeroom.
_______________________________________________________________________
4. Survey every 10th student who enters the school on Monday morning.
This is a random sample. Everyone in the school (the population) has an equal
_______________________________________________________________________
_______________________________________________________________________
chance of being chosen.