Continuous variables are numerical values that can take on an infinite number of possibilities within a given range. They can be measured and can include fractions or decimals. Examples of continuous variables include height, weight, and temperature, as these can vary smoothly and can be expressed with great precision. In statistics, continuous variables are often analyzed using various methods, such as mean, median, and standard deviation. These variables are essential in fields like science, economics, and healthcare, where precise measurements are crucial for understanding trends and making informed decisions.