Population and Variable – Introduction to Statistics

Practice of Statistics – Population and Variable

Population and variable are discussed in this chapter – Introduction to Statistics


Population

The entire group of individuals to be studied is called the population. An individual is a person or object that is a member of the population being studied.


A polling organization contacts 1294 teenagers who are 16 to 19 years of age and live in North America and asks whether or not they had driven a car on a highway recently.
What is the population in the​ study?

Teenagers who are 16 to 19 years of age and live in North America.


A polling organization contacts 1294 teenagers who are 16 to 19 years of age and live in North America and asks whether or not they had driven a car on a highway recently.
What is the sample in the study?

The 1294 teenagers who are 16 to 19 years of age and live in North America.


A​ quality-control manager randomly selects 60 bottles of soda that were filled on June 14 to assess the calibration of the filling machine.
What is the population in the​ study?

Bottles of soda produced in the plant on June 14.


A​ quality-control manager randomly selects 60 bottles of soda that were filled on June 14 to assess the calibration of the filling machine.
What is the sample in the study?

The 60 bottles of soda selected in the plant on June 14.


Descriptive statistics consists of organizing and summarizing information collected.

Descriptive


Inferential statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.

Inferential


Is a numerical summary of a sample, which is a subset of the population that is being studied.

Statistics is the science of​ collecting, organizing,​ summarizing, and analyzing information to draw a conclusion and answer questions. In​ addition, statistics is about providing a measure of confidence in any conclusions.

Statistic


Is a numerical summary of population, which is an entire group to be studied.

Parameter


Are the characteristics of the individuals within the population. If variables did not vary, they would be constants, and statistical inference would not be necessary.

Variables


Determine whether the underlined value is a parameter or a statistic.
Following the election, 18 % of the governors of all 50 areas of a country were female.
Is the value a parameter or a​ statistic?

The value is a parameter because the governors of all 50 area of a country are a population.


Determine whether the underlined value is a parameter or a statistic.
In a national survey on substance abuse, 66.4 % of respondents who were full-time college students aged 18 to 22 reported using alcohol within the past month.
Is the value a parameter or a​ statistic?

The value is a statistic because the respondents who were full-time college students aged 18 to 22 are a samply


Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning.
For a certain movie, 64.3 % of the 112 members of the audience were females.

Parameter, because the data set of all 112 audience members is a population


Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning.

In a certain soccer league, 43 % of the 14 teams had won more games than they had lost.

Parameter, because the data set of all 14 teams is a population


Determine whether the underlined value is a parameter or a statistic.
In a championship football game, a quarterback completed 59% of his passes for a total of 265
yards and 2 touchdowns.
Is the value a parameter or a​ statistic?

The value is a parameter because the quarterback’s passes are a population.


Determine whether the underlined value is a parameter or a statistic.
One of the greatest baseball hitters of all time has a career batting average of 0.366.
Is the value a parameter or a​ statistic?

The value is a parameter because the career at-bats of a baseball player are a population


Qualitative

Pertaining to or concerned with quality or qualities.

Qualitative variables allow for classification of individuals based on some attribute or characteristic.


Favorite musical band

The variable is qualitative because it is an attribute characteristic


Favorite Song

The variable is qualitative because it is a attribute characteristic


Quantitative

That is or may be estimated by quantity.

Of or relating to the describing or measuring of quantity.

Quantitative variables provide numerical measure of individuals and can be added or subtracted and provide meaningful results
.


Age of car driver

The variable is quantitative because it is a numerical measure.

Number of cars owned

The variable is quantitative because it is a numerical measure.


Determine whether the variable is qualitative or quantitative.
Gallons of water in a swimming pool
Is the variable qualitative or​ quantitative?

The variable is quantitative because it is a numerical measure.


Determine whether the variable is qualitative or quantitative.
Height
Is the variable qualitative or​ quantitative?

The variable is quantitative because it is a numerical measure.


Determine whether the variable is qualitative or quantitative.
Breed of cat.
Is the variable qualitative or​ quantitative?

The variable is qualitative because it is an attribute characteristic.


Determine whether the variable is qualitative or quantitative.
Zip code.
Is the variable qualitative or​ quantitative?

The variable is qualitative because it is an attribute characteristic.


Determine whether the variable is qualitative or quantitative.
Number of cars owned.
Is the variable qualitative or​ quantitative?

The variable is quantitative because it is a numerical measure.


Discrete

A variable that may assume only a countable and usually finite, number of values.

A discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values. The term​ “countable” means that the values result from​ counting, such as​ 0, 1,​ 2, 3, and so on.


Continuous

Uninterrupted in time; without cessation.

A continuous variable is a quantitative variable that has an infinite number of possible values that are not countable.


Determine whether the quantitative variable is discrete or continuous.
Number of days of rainfall in a year.
Is the variable discrete or​ continuous?

The variable is discrete because it is countable


Determine whether the quantitative variable is discrete or continuous.
Volume of liquid in a glass.
Is the variable discrete or​ continuous?

The variable is continuous because it is not countable.


Determine whether the quantitative variable is discrete or continuous.
Touchdowns thrown by a quarterback.
Is the variable discrete or​ continuous?

The variable is discrete because it is countable


Determine whether the quantitative variable is discrete or continuous.
Volume of water in a reservoir.
Is the variable discrete or​ continuous?

The variable is continuous because it is not countable.


Variable

A value or characteristic changes among members of the population.


Interval

A variable is at the interval level of measurement if it has the properties of the ordinal level of measurement and the differences in the values of the variable have meaning.
A value of zero in the interval level of measurement does not mean the absence of the quantity. Arithmetic operations such as addition and subtraction can be performed on values of the variable.


Ratio

A variable is at the ratio level of measurement if it has the properties of the interval level of measurement and the ratios of the values of the variable have meaning. A value of zero in the ratio level of measurement means the absence of the quantity. Arithmetic operations such as multiplication and division can be performed on the values of the variable.


Nominal

A variable is at the nominal level of measurement if the values of the variable​ name, label, or categorize.
In​ addition, the naming scheme does not allow for the values of the variable to be arranged in a ranked or specific order.


Ordinal

A variable is at the ordinal level of measurement if it has the properties of the nominal level of​ measurement, but the naming scheme allows for the values of the variable to be arranged in a ranked or specific order.


Determine the level of measurement of the variable.

Ranks of scores in a tournament.

Choose the correct level of measurement.

Ordinal


Determine the level of measurement of the variable below.

Volume of water used by a household in a day.

Choose the correct answer below.

Ratio


Determine the level of measurement of the variable.

Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years.

Ratio


Determine the level of measurement of the variable below.

Eye color

——



Choose the correct answer below.

Nominal


Determine the level of measurement of the variable below.

Time of day measured in military time.

Choose the correct answer below.

Interval


Determine the level of measurement of the variable.

Monthly temperatures: 61 degrees F, 65 degrees F, 69 degrees F, 73 degrees F, and 77 degrees F

Choose the correct answer below.

Interval


Individual

An individual is a person or object that is a member of the population being studied.


Explain what is meant when it is said that​ “data vary”. How does the variability affect the results of statistical​ analysis?

When we say​ data vary it means that the values of the variable change from individual to individual. Furthermore, certain variables can change over time for certain individuals. Because data​ vary, two different statistical analysis of the same variable can lead to different results.Similar individuals will not necessarily yield the same data. People can be different​ heights, different​ weights, different​ ages, and so on. In addition to​ this, a​ person’s age will change over​ time, and their height and weight can change over time as well. Measuring two​ people’s heights at the same​ time, or measuring one​ person’s height at different times can yield different results.


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