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N.K. Sharma
Asked: 2024-01-21T16:05:27+05:30

Differentiate between discrete and continuous variable.

Differentiate between discrete and continuous variable.

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      Criteria Discrete Variable Continuous Variable
      Definition A variable that can only take on specific, distinct values within a defined range, often in the form of whole numbers or categories. A variable that can take on an infinite number of values within a defined range, often measured with decimal precision.
      Nature of Values Values are countable, separate, and distinct from each other. Values form a continuous range without gaps or intervals, and can be measured to any level of precision.
      Examples Number of students in a classroom, number of cars in a parking lot, the outcome of rolling a die. Height, weight, temperature, time, and distance are continuous variables.
      Data Type Typically, discrete variables are categorical or nominal, but they can also be ordinal. Continuous variables are usually ratio or interval scale, allowing for mathematical operations like addition and subtraction.
      Graphical Representation Shown as bar charts, histograms, or pie charts to depict the frequency or distribution of each distinct value. Represented using line graphs, scatter plots, or density plots to illustrate the continuous distribution of data points.
      Statistical Analysis Analyzed using techniques like frequency distributions, cross-tabulations, and chi-square tests. Analyzed using statistical methods like means, medians, standard deviations, and correlation analysis.
      Probability Density Discrete probability mass function assigns probabilities to each specific value, resulting in a probability distribution. Continuous probability density function assigns probabilities to ranges of values, resulting in a probability density curve.
      Measurement Precision Limited to specific values without intermediate values. Offers a high level of measurement precision with infinite possible values between any two points.
      Example Applications Counting occurrences, tracking categorical data, analyzing survey responses, or modeling finite events. Measuring physical attributes, analyzing scientific data, modeling natural processes, or understanding continuous phenomena.
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