Statistics 1.1-1.2: Sampling and Types of Data

MATH 1402 Aleks 1.1-1.2 terms and example questions.

Statistics

The study of procedures for collecting, describing, and drawing conclusions from information

Population

The entire collection of individuals about which information is sought

Sample

A subset of a population containing the individuals that are

Simple Random Sampling

Every option has an equal chance to be picked

A physical education professor wants to study the fitness levels
of 20,000 students at her university. She numbers the students
from 1 to 20,000, then uses a random number generator to
select 100 students to participate in the study. What type of sample is this?

Simple random sample

Sample of convenience

One is selected without following a well-defined random process

A restaurant manager stops by the tables of people in the restaurant and asks them for their opinions on upcoming menu changes. What type of sample is this?

Sample of convenience

Stratified random sampling

The population is divided into groups (strata) and a simple random sample is drawn from each group (stratum)

A company with 800 full-time and 200 part-time employees wants to draw a sample of 100. They select a simple random sample of 80 full-time employees and 20 part-time employees. What type of sample is this?

Stratified random sampling

Cluster sampling

Items are randomly selected in groups; Population is divided into groups and the sample is the randomly picked whole groups

Every 10 years, the U.S. Census Bureau counts everyone living in the U.S. To verify accuracy in a specific city, they sample census districts and recount the people in those districts. What type of sample do these recounted individuals form?

Cluster sample

Systematic sampling

Items are ordered, and every kth item is selected for the sample.

(3,8,13,18,23…) Start at 3 and go every 5th item

Systematic sampling

A college basketball team held a promotion at one of its games in which every twentieth person who entered the arena won a free basketball. What type of sample do the winners represent?

Systematic sampling

Voluntary response samples

Often used by the media to engage with the audience

A radio announcer invited people to call the station and tell what they think

Voluntary response sample

Statistic

A number that describes a sample

Parameter

A number that describes a population

57% of the teachers at Mary Persons HS are female. What does the number 57% describe?

A parameter, because it describes the entire population of teachers in the school.

In a sample of 100 surgery patients who were given a new pain reliever, 78% of them reported significant pain relief. What does the number 78% describe?

A statistic, because it describes the sample.

Individuals

What the information is collected on

Variables

The characteristics of the individuals about which we collect information; Qualitative and quantitative

Data

The values of the variables

Data set

The information collected

Qualitative variables

Classify individuals into categories

Quantitative variables

Tell how much or how many of something there is

A person’s place of birth describes which variable?

Qualitative variable, because places can included categories like “New York” or “Atlanta”

A person’s age describes which variable?

Quantitative, because it tells how much time has elapsed since the person was born

The mileage of a car describes which variable?

Quantitative, because it tells how many miles a car will go on a certain amount of gasoline.

The color of a car describes which variable?

Qualitative, because it consists of categories of different colors.

Ordinal variables

Part of qualitative variables. Have a natural ordering

Nominal variables

Part of qualitative variables. Do not have a natural ordering

Discrete variables

Part of quantitative variables. Possible values can be listed or counted.

Continuous variables

Part of quantitative variables. Can take on any value within a given interval.

State of residence describes which qualitative variable?

Nominal, because there is no natural order to the states

Hair color describes which qualitative variable?

Nominal, because there is no natural order to hair colors

Letter grade in a class describe which qualitative variable?

Ordinal, because there is a natural ordering (A, B, C, D, or F)

Size of drink describes which qualitative variable?

Ordinal, because there is a natural ordering (Large, medium, small)

Age of a person on their last birthday describes which quantitative variable?

Discrete, because a person’s age at their birthday can be listed

Height of a person can be described by which quantitative variable?

Continuous, because height can take on any value in an interval

Number of siblings a person has can be described by which quantitative variable?

Discrete, because the number of siblings can be listed

Distance a person commutes to work can be described by which quantitative variable?

Continuous, because distance can take on any value in an interval