### 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.

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.

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.**