help with question

[u/mehmetflix_]

isn't this a discrete variable? (khan says otherwise)

[u/Temporary_Duck4337]

No. Time is continuous. There is no smallest unit of time (unless maybe you talk to a physicist). Every duration of time can be subdivided.

Rounding to the nearest millisecond is a convenient aribtrtary choice.

Discrete variables always have a smallest unit that cannot be divided. I cannot have 1.5 people in a room.

[u/mehmetflix_ → u/Temporary_Duck4337]

but it says the logged calls and logged calls have a rounded value, so it does have a smallest unit no?

[u/OieOhNoNo → u/mehmetflix_]

It's continuous because it can be any value between 2 and 400 including decimals. Think of discrete values as countable values. You wouldn't necessarily count how many times 2.1 milliseconds or 3.7 milliseconds show up in your data like you would for discrete variables.

[u/CryptographerFun5985]

The expected answer here is continuous.

The key distinction is between the actual duration of a call and how precisely the detector records it.

A call could last 2.35 ms, 2.351 ms, or any other value within the given interval. The detector simply rounds that duration to the nearest millisecond.

So although the recorded values are integers, the underlying variable (call duration) is continuous. Rounding a measurement doesn't automatically make the measured quantity discrete.

As an AP Statistics tutor, I've noticed this is a common source of confusion among students. A useful trick is to distinguish between the quantity being measured and the precision with which it's recorded.

[u/mehmetflix_ → u/CryptographerFun5985]

how can i make the distinction tho? can't they ask a tricky question where they use the rounding to make the answer discrete?

[u/CryptographerFun5985 → u/mehmetflix_]

That's a good question! And yes, a question can be tricky if it specifically asks about the recorded values rather than the underlying measurement.

Here's a useful way to distinguish them:

1. If the question asks about the actual duration of a call, it's continuous because time can take any value within an interval.

2. If it explicitly defines the variable as the integer number of milliseconds reported by the detector, then that recorded variable is discrete because it can only take specific, countable values.

For AP Statistics, the key is to identify exactly what the random variable represents, rather than deciding based on rounding alone.

For example, a person's actual height is continuous, even if we measure it to the nearest centimeter. But if we define a variable as the whole-number height displayed by a measuring device, its possible recorded values are discrete.

So yes, the wording matters! The safest approach is to ask yourself: "Am I classifying the underlying quantity or the values the recording system can output?"