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Consider the following statements: 1. A continuous random variable can take all values in an interval. 2. A random variable which takes a finite number of values is necessarily discrete. 3. Construction of a frequency distribution is based on data which are discrete. Which of the above statements are correct?

Consider the following statements: 1. A continuous random variable can take all values in an interval. 2. A random variable which takes a finite number of values is necessarily discrete. 3. Construction of a frequency distribution is based on data which are discrete. Which of the above statements are correct? Correct Answer 1, 2 and 3

Observations:

1) The statement "A continuous random variable can take all values in an interval" is correct because A continuous random variable is a random variable where the data can take infinitely many values.

2) The statement "A random variable which takes a finite number of values is necessarily discrete." is correct because a discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........

3) The statement "Construction of a frequency distribution is based on data which are discrete." is correct because we can not find frequency distribution if the data is continuous, hence the data is discrete.

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