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Quantitative variables are an essential part of descriptive statistics. They represent variables that can be measured and expressed numerically. Unlike qualitative variables, which describe categories or classes, quantitative variables allow us to perform arithmetic operations like addition and subtraction.

In the context of our exercise, the variable of interest is 'miles per gallon' (mpg), which measures how far a vehicle can travel per gallon of fuel. Since mpg is measurable and expressed in numbers, it is a quintessential example of a quantitative variable.

• Quantitative variables can be discrete or continuous.
• Discrete quantitative variables take specific values, like the number of cars.
• Continuous quantitative variables can take any value within a range, like mpg.

The importance of quantitative variables lies in their ability to help make precise and detailed analyses of observations through various statistical methods.

Random sampling is a cornerstone of reliable statistical analysis. It involves selecting a subset of individuals from a population in such a way that every individual has an equal chance of being chosen.

In the exercise at hand, a random sample of 35 new cars was selected from the larger population of all new cars. This method ensures that the sample accurately reflects the diversity within the entire population. Random sampling reduces bias and increases the reliability of the results.

• Ensures that the sample is representative of the population.
• Helps in making inferences about the population.
• Minimizes bias and systematic errors.

Employing random sampling is crucial for deriving valid insights from the data, as it allows for generalization from the sample to the population.

Identifying the population is a vital first step in any statistical study. The population refers to the complete set of items or individuals from which data is drawn.

In the scenario presented in our exercise, the population is all new cars. This identification is crucial because it determines the scope and applicability of the study's findings. Understanding the population helps in defining the context and potential limitations of a statistical analysis.

• The population contains all elements that could be studied.
• The objective is to generalize the findings from the sample to the population.
• Incorrect identification can lead to irrelevant or misleading conclusions.

Recognizing the correct population ensures that conclusions drawn from the sample are both valid and applicable to the larger group of interest.