# Why is second question false?

When we create the distribution the percentile numerical value indicates the rank of the value. So why is it false?
The hint though explains it but the ques just indicates the literal meaning for numerical value !

I tried understanding from the external link but couldn’t so, I posted my the query!

The Percentile Rank is not a numerical value. It is a categorical value with a set order. Therefore it is an ordinal data. For example, 20th percentile comes before 80th percentile. And 20th percentile is a position below which 20% of the observation can be found.

Best,
Sahil

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@Sahil is correct. The percentile rank of a score,P(x) is the categorica and not numeral value
that has p% of the values at or below it.

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Here is the source.

‘A numerical variable is similar to an ordinal variable, except that the intervals between the values of the numerical variable are equally spaced’

I guess Dataquest didn’t cover numerical data. It is very similar to ordinal, but there is that little difference: the spaces between then are equal.

Conclusion: as I can understand from this definition, question 2 should be True. The space between one and another are equal, they vary by percentual points which aggregates the same amount of data.

Why am I wrong?

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"A numerical variable is similar to an ordinal variable, except that the intervals between the values of the numerical variable are equally spaced"

That’s a fair point. So let me give you another example.

For example, suppose you receive a survey from your favorite restaurant that asks you to provide feedback on the service you received. You can rank the quality of service as “1” for poor, “2” for below average, “3” for average, “4” for very good and “5” for excellent. The data collected by this survey are examples of ordinal data. Here the numbers assigned have an order or rank; that is, a ranking of "4” is better than a ranking of “2.”

However, even though you have assigned a number to your opinion, this number is not a quantitative measure: Although a ranking of “4” is clearly better than a ranking of “2,” it is not necessarily twice as good. The numbers are not mathematically measured or determined but are merely assigned as labels for opinions.
https://sciencing.com/difference-between-nominal-ordinal-data-8088584.html

As you can see, all of the values are equally spaced, yet we can only consider it as ordinal data. In the same way, Percentile Ranks are just labeled numerical positions below which a certain percent of observation can be found.

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I am uncertain if Percentile Ranks are equally spaced.

Because you can have a Percentile Rank of 80 and 20. They are not equally spaced so they can’t be numerical variables, right?

On the other hand, Quartiles are equally spaced, but those are, as you (Sahil) put it - labeled numerical positions and should not be numerical variables based on that definition (and the article you shared). Is that correct?

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Percentile ranks are equally spaced in the sense that the distance between percentiles (10, 20), (20,30)… etc are equal on a graph. However, they are not numerical, they are numerical labels, so the distance doesn’t matter here.

Yes, just like the percentile rank case, distance doesn’t matter here as they are actually position labels.

Best,
Sahil

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