Discrete and Continuous Data Question (1 Viewer)

[gotogo.gogo]

Hi! I was wondering if these variables:

• Field-goal percentage: Field goals made divided by field goal attempted
• Free throw percentage: Free throw made divided by free throw attempted

Are considered discrete or continuous. I've done some research and it states that percentages are considered continuous, however, if the underlying data its collected from is discrete, does this still make it continuous.

 

[cossine]

Hi! I was wondering if these variables:

• Field-goal percentage: Field goals made divided by field goal attempted
• Free throw percentage: Free throw made divided by free throw attempted

Are considered discrete or continuous. I've done some research and it states that percentages are considered continuous, however, if the underlying data its collected from is discrete, does this still make it continuous.

What matter is the random event that you are considering the probability of. If you plot the random events with the probabilities on a graph would you have a continuous line like y=x.

 

[gotogo.gogo]

What matter is the random event that you are considering the probability of. If you plot the random events with the probabilities on a graph would you have a continuous line like y=x.

sorry i dont get it

 

[Drongoski]

1st continuous; second(Free Throws) discrete. Not being well versed with Basketball: you can be awarded 1, 2 or 3 free throws. So you can, if awarded 3 throws, you can score 0, 1, 2 or 3: so the percentage can be 0/3, 1/3, 2/3 or 3/3 [x 100%] - only 4 (a finite and countable number, you can tell them apart, individually). If this percentage can span a continuum of possibilities (like gender fluidity), from 0 to 1, then you have a continuous variable.

 

[cossine]

sorry i dont get it

There two main types ways to model probability, probability mass function and probability density function. So what you could do is model the field goal percentage using a binomial distribution. The binomial distribution is discrete, discrete meaning opposite of continuous.

Now probabilities can take any value between [0, 1]. However what we are concerned about is the domain. Does domain consist of categorical variables or is the domain some subset of real numbers? The domain of the probability disstribution will determine whether something is discrete or continuous.

There should be in your math textbook examples of various probability mass functions and density functions.

 

[chilli 412]

1st continuous; second(Free Throws) discrete. Not being well versed with Basketball: you can be awarded 1, 2 or 3 free throws. So you can, if awarded 3 throws, you can score 0, 1, 2 or 3: so the percentage can be 0/3, 1/3, 2/3 or 3/3 [x 100%] - only 4 (a finite and countable number, you can tell them apart, individually). If this percentage can span a continuum of possibilities (like gender fluidity), from 0 to 1, then you have a continuous variable.

aren't both discrete? since both are in the form of p/q for integers p,q which implies that both variables are rational numbers, which means that the data set cannot theoretically take any value (in the set of real numbers), such as sqrt2 for example

 

[chilli 412]

but that's just with the basic definition of continuous vs discrete variables i was taught, there is probably a more rigorous definition that goes against what i said

 

[cossine]

cannot theoretically take any value (in the set of real numbers), such as sqrt2 for example

You could in theory have set random variables {1, sqrt(2), 5}. With some arbitrary probabilities. Sketching this plot with give function that looks like bunch of dots. Of course for visualization purposes a bar graph will be used.

There is formal definition of countability which can be used to classify whether a set is discrete or continuous. However, I believe outside the scope of high school math. You will learn about this if you decide to study discrete math.

 

[chilli 412]

You could in theory have set random variables {1, sqrt(2), 5}. With some arbitrary probabilities. Sketching this plot with give function that looks like bunch of dots. Of course for visualization purposes a bar graph will be used.

There is formal definition of countability which can be used to classify whether a set is discrete or continuous. However, I believe outside the scope of high school math. You will learn about this if you decide to study discrete math.

but for the case of Field goals made divided by field goal attempted, or Free throws made divided by free throw attempted, how could you ever get a result of sqrt2 ?

 

[cossine]

but for the case of Field goals made divided by field goal attempted, or Free throws made divided by free throw attempted, how could you ever get a result of sqrt2 ?

My previous post is not related to that but to the domain of a probability mass function.

 

[yanujw]

but for the case of Field goals made divided by field goal attempted, or Free throws made divided by free throw attempted, how could you ever get a result of sqrt2 ?

Continuous variables are not neccessarily variables that can take irrational values. Remember that there are infinitely many rational numbers also.

 

[chilli 412]

Continuous variables are not neccessarily variables that can take irrational values. Remember that there are infinitely many rational numbers also.

i thought continuous variable were those that could take any value on the number line. but if we show that this variable can't take a value of sqrt2, which lies on the number line, the variable must not be a continuous variable. am i right in saying this?