mr. gonzalez algebra 2 intro to statistics. population and sample what’s the difference? a...

MR. GONZALEZALGEBRA 2

Intro to Statistics

Population and Sample

What’s the difference? A population is all the members of a set. A sample is part of a population

Example Population: Mater Academy Sample: Class of 2018

Different Sampling Methods

Convenience SampleSelf-Selected SampleSystematic SampleRandom Sample

Convenience Sample

For a convenience sample, select any members of the population who are conveniently and readily available

Example Mr. G takes a sample of the students in his class

Self-Selected Sample

For a self-selected sample, select only members of the population who volunteer for the sample study.

Example Mr. G invites students to come after school to do a

study in his classroom

Systematic Sample

For a systematic sample, order the population in some way, and then select from it at regular intervals

Example Mr. G gives all his students a number from 1 to 180,

but then he only uses students who’s numbers are multiples of 3

Random Sample

In a random sample, all members of the population are equally likely to be chosen

Example Mr. G walks around the halls and picks 50 random

students to make a sample

Bias

A sample has a bias when a part of a population is overrepresented or underrepresented

A bias is a systematic error introduced by the sampling method

Example Mr. G does a survey about exercising after school.

More than half of the sample are athletes in the school

Study Methods

Observational StudyControlled StudySurvey

Observational Study

In an observational study, you measure or observe members of a sample in such a way that they are not affected by the study

Example Mr. G, does a study of his class. He observes if there is

a connection to the students that did not pass his first test and the students that did not do their homework.

Controlled Experiment

In a controlled experiment, you divide the sample into two groups. You impose a treatment on one group but not the other “control” group. Then you compare the effect on the treated and the control group.

Example Mr. G reviews for an test with period 1 and not with

period 2. After the test, he compares the results of the two classes.

Survey

In a survey, you ask every member of the sample a set of questions.

Example Mr. G asks all his classes a series of questions

pertaining to the last test they took in class

Practice Questions

What is the sampling method used for each situation? Does the sample have a biased?

1. A newspaper article on the tax increase invites readers to express their opinions on the newspapers' website.

2. A reporter interviews people leaving the city’s largest park

3. A survey service calls every 50th listing from the local phone book

Practice Question Answers

1. A newspaper article on the tax increase invites readers to express their opinions on the newspapers' website.

Self-selected sample. It might have a bias, depending on who visits the website.

2. A reporter interviews people leaving the city’s largest park

Convenience sample. It might have a bias, depending on what the study was about.

3. A survey service calls every 50th listing from the local phone book

Systematic Sample. It might have a bias, depending if there is a connection between the people who are listed or not listed

Practice Questions

Which type of study method is described in each situation? Should the sample statistics be used to make a general conclusion about the population?

1. Researchers randomly choose two groups from 10 volunteers. Over a period of 10 weeks, one group eats ice cream before going to sleep, and the other does not. Volunteers were monitoring devices while sleeping, and researchers record dream activity.

2. Students in a science class record the height of bean plants as they grow.

Practice Question Answers

1. Researchers randomly choose two groups from 10 volunteers. Over a period of 10 weeks, one group eats ice cream before going to sleep, and the other does not. Volunteers were monitoring devices while sleeping, and researchers record dream activity.

Controlled study. The statistics are based on such a small sample that they are not reliable as a general conclusion.

2. Students in a science class record the height of bean plants as they grow.

Observational study. The statistics may provide a general conclusion but may not be reliable based the type of soil, sunlight, water, and fertilization