Answer: Discrete and continuous variables are distinguished by their characteristics, as follows:
Discrete Variables:
Consist of individual, distinct values that are countable and finite.
Can take only specific numerical values within a given range or interval.
Do not have intermediate values or decimals.
Examples include number of children in a family, number of cars in a parking lot, and number of heads in a coin toss.
Continuous Variables:
Consist of uncountable and infinite values that can take any value within a given range or interval.
Can take on fractional or decimal values and have infinitely many possible intermediate values.
Have an infinite number of values that lie between any two points.
Examples include height, weight, time, and temperature.
The attributes that distinguish discrete and continuous variables are determined by the nature of the underlying data. Discrete variables arise from countable events or phenomena, where there is a fixed and finite set of possible outcomes. They are typically associated with whole numbers or integers, such as counts or tallies.
Continuous variables, on the other hand, arise from measurements or observations that can take any value within a range or interval. They are typically associated with physical or continuous phenomena, where there is a continuum of possible outcomes that can be measured with increasing precision.
In summary, the attributes that make variables discrete or continuous are related to their countability, range of possible values, and presence of intermediate values. These attributes are determined by the underlying nature of the data and the type of phenomena being measured or observed.
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