# Data Type

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• #54455

Lokeshwaran TK
Member

Hello,
Is 77.27% Discrete (or) Continuous. (kindly read the below note before answering)

CSAT = (# of Sat)/(# of Survey); (here 17/22 = 77.27%)

Initially I was given to understand that any number with decimal value (or) percentage will fall under Continuous category. In one of my recent training, I was advised that we should look at numerator and denominator. In this case as both numerator and denominator are discrete, the output 77.27% is also discrete.

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#195456

Prabhu V
Participant

Hi,

https://www.isixsigma.com/topic/continuous-data-and-discrete-data-37/

https://www.isixsigma.com/topic/continuous-data-and-discrete-data/

Best regards
Prabhu V.

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#195458

Robert Butler
Participant

You can treat it as continuous. The recent thread below has the details.

https://www.isixsigma.com/topic/cycle-count-attribute-or-variable/

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#195463

MBBinWI
Participant

@tklokesh – Are both your numerator and denominator whole numbers and of a fixed number (i.e.; # of surveys is limited to 10, # sat is a whole number between 0 and 10)? If so, then technically you have a discrete sample set which would comprise the values 0 to 1.0 in incremental steps of 0.1. These would be the only viable items in the data set, and as such, regardless of the fact that these values are decimals, they are discrete. Merely being a decimal does not make a value continuous.

More generally, all data sets are technically discrete, as we must limit the number of divisions to the right of the decimal at some point. Thus, we always limit the number of possible values in the data set (although each successive position increases the set by a factor of 10). The more important characteristic to evaluate is whether the number of divisions available is sufficiently larger than the number of divisions required to make a decision. Let’s say that I’m willing to make a decision based on a value at the tenths place (10.1 is good, 10.2 is bad). If I then have measurements that are meaningful at the hundredths (or even smaller) level, then I can be confident that I have a sufficiently continuous level (many more divisions of values than decision level). Likewise, if I am deciding to use the tenths position and my measured values are only to the tenths place but range from 10.1 to 1000.1 in a uniform distribution, with the decision point at 50.0 then the tenths place really becomes insignificant compared to the data set and so can be considered continuous.

Finally, consider the data set that has 1000 values at 10.11111, 1000 values at 10.22222, and 1000 values at 10.33333. While you have a relatively large data set (3000 values), and at a very high level of precision (a hundred-thousandth), you really only have 3 levels and if you need to separate into more than 3 levels, you are incapable of doing so.

Sorry, but like most MBB answers, this falls into the “it depends” category. Whomever taught you that a decimal = continuous (and the converse, no decimal = discrete) was too simplistic. Hopefully this description helps.

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#195465

Chris Seider
Participant

@tklokesh

Why are you asking? As @MBBinWI stated, how you treat it depends on your needed application. I’ve heard some folks imply if the numerator or denominator are counts, then you must treat the % as a discrete number but I advise folks to just treat it as continuous UNLESS, as @MBBinWI suggested, you have an issue such as a small number of potential answers or small sampling and then you can used other techniques to show improvement/analysis like chi-squared.

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#195489

Lokeshwaran TK
Member