What is a Density Curve?

What is a density curve?

Which of the following statements best describes a density curve?

A. A density curve of a variable represents the distribution of a discrete variable.

B. A density curve of a variable represents the approximate distribution of a continuous variable.

C. A density curve of a variable represents the distribution of the variable.

D. A density curve of a variable is a smooth curve with which one can identify the shape of the distribution of the variable.

Answer:

The correct answer is C. A density curve of a variable represents the distribution of the variable.

Explanation: A density curve is a smooth curve that represents the distribution of a continuous variable, often visualized using a probability density function. The area under the curve represents probability and sums to one.

What is a Density Curve?

A density curve is a smooth curve that represents the distribution of a continuous random variable. The total area under this curve is always one, representing the entire possible range of data which these variables can take on. For instance, the normal distribution, also known as the bell-shaped curve, is a common example of a density curve used across various disciplines due to its characteristic properties.

A density curve can depict different types of probability distributions such as uniform, normal, or skewed distributions, all with areas adding up to one. With the help of the probability density function (pdf), a density curve can be visualized, and the area under the curve between two values gives the probability of the variable falling within that range. This is a significant aspect of continuous probability distributions in contrast to discrete distributions which deal with countable outcomes.