my teacher said that stars are infinite so they are continuous variable... I agree they are infinite but they are in whole numbers so why are not they discrete variable... like number of stars and number of books are same in counting both are counted and stars are not measured they are counted so why are not they discrete variable... please answer

Stars and books are continuous variables because their number can have any value.

Discrete variables must fall into a specific range.

For example: On a scale of 1-10. The answer must fall somewhere between 1 and 10. 12 is NOT a valid response.

I'm afraid to say that the above post is not accurate.

Discrete data can take only exact values.

Books are discrete because you cannot have a book and a half... not unless it was ripped apart.

Continuous data cannot take exact values but can be given only within a specified range or measured to a specified degree of accuracy.

For example, if you measure something with a ruler, say, 15 cm. That's the closest reading, rounded to 1 cm. This value could have very well been any value within the interval 14.5 to 15.5 cm.

This said, you cannot say for sure how many stars there are. You could for example see 100 stars within a certain that you see, but there could be other stars that you cannot see (one closer star hiding another, or a cloud of dust between you and the star, etc). So, 100 is an approximation of the number of stars that you see. Hence, we take it as a continuous data.

I was trying to reword this definition. Sounded like I didn't do a good job of it. Sorry. :(

"A discrete variable is one that cannot take on all values within the limits of the variable. For example, responses to a five-point rating scale can only take on the values 1, 2, 3, 4, and 5. The variable cannot have the value 1.7. A variable such as a person's height can take on any value. Variables that can take on any value and therefore are not discrete are called continuous."