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Discrete or Continuous?

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  • #38073

    Ripley
    Member

    We are having a heated discussion about whether data that we have is continuous or discrete.  We are looking at number of calls coming into the Contact Center on a daily basis and want to lay those daily totals on a control chart.
    Is this continuous or discrete data?
    Thanks!!!

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    #113472

    Bob J
    Participant

    Hi Ripley,
    Since it’s count data it’s discrete…
    Have a good weekend!
    Best Regards,
    Bob J

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    #113474

    Darth
    Participant

    It depends…don’t u just luv that answer.  In certain situations, discrete data may take on characteristics of continuous data.  Bob J was correct in that the underlying count is discrete.  But, if counts are large, distribution of values are relatively wide, and the the values are distributed across the values, you can “pretend” it is continuous and use the appropriate tools.

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    #113475

    shree
    Member

    it is continous

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    #113478

    Ripley
    Member

    Sure, thanks, guys and girls, now I’m more confused!  LOL
    Your responses have me thinking  (which may or may not be a bad thing in my case!), if daily call volume is, in fact, discrete, then what type of data is delivery time in days?  We have been treating this as continuous data.  Have we been treating delivery time as the wrong type of data all along (insert gasp here)?

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    #113479

    Kung Fu Joe
    Participant

    It is continuous. If  you look at the spectrum of in coming calls, you primarily measure them based on units of time. Time itself is measured on a continuum and therefore can’t be considered attribute.

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    #113481

    Kung Fu Joe
    Participant

    It is continuous. If  you look at the spectrum of in coming call you primarily measure them based on units of time. Time itself is measured on a continuum and therefore can’t be considered attribute.

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    #113482

    Ripley
    Member

    Kung Fu:
    I absolutely agree about time being continuous, but what we are measuring is total number of calls per day and then laying that on a control chart.

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    #113483

    luke skywalker
    Participant

    What you might do to add some sense of confidence in your treatment of discrete data as continuous would be to actually look at it in a histogram. That would illustrate Darth’s point of having the data spread across its full range. From there you might try fitting your data to a known distribution, which might help. Keep in mind that lots of folks rush to call discrete data continuous so all the stats tools and tests will be available – but many have an assumption of normality, so you will increase your risk of making an incorrect conclusion. Normal is continuous, but not all continuous data is normal.
    Most of the computer software out there can help fit distributions… 

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    #113484

    Bob J
    Participant

    Ripley,
    Depends a lot on the characteristics of the data… 
    If you are tracking actual times (5.321 days for example) then it is continuous…. 
    If you count entire days (5 days) then it is discrete…. 
    If you have a very large sample, as Darth pointed out, it’s really discrete but can be treated as continuous without too much error…
    Hope this helps…
    Best Regards,
    Bob J

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    #113486

    Darth
    Participant

    Hey Luke, hope all is well and glad to see you posting again.   Hope your holidays were good.  Must be test day since you have time to post.  I still owe you a phone call to catch up.  talk to you soon.
    Daddy Darth
     

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    #113487

    Bob J
    Participant

    Darth,
    Good to see you up and about….  Your insight is always appreciated…
    Have a great weekend!
    Best Regards,
    Bob J

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    #113488

    Darth
    Participant

    thanks Mike.  has anyone seen Stan?  it has been so quiet without him.  maybe that’s a good thing.  i know, he is out still trying to find that great bottle of tequila he promised me.  talk 2 ya later.

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    #113491

    Thai
    Participant

    Assuming Stan was refering to the Clinton River in Michigan when he said… “Casa de Stans by the beautiful Clinton River was the scene of a wonderful Christmas…” he may be out sandbagging as the Clinton River was flooding in places this morning…
    Kirk

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    #113496

    Darth
    Participant

    Thanks for the report.  Yes, I understand the front 30 acres have a tendency to flood.  It may have washed out the bridge.

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    #113504

    Gabriel
    Participant

    Ripley,
    Let’s see if this helps to confuse you more.
    DATA IS ALWAYS DISCRETE.
    See. Say you are measuring the diameter of some steel balls. Clearly, the diameter of the balls is a continous VARIABLE. Continous means infinite possible values between any two values. Continous means that the exact value can never be written down because you would need an infinte number of decimal places. Continous means that you will never get two identical values. And while all this applies to the balls diameters, nothing of this applies to the DATA you can get measuring the balls diameters. Why, because your instrument does not have infinite resolution, in never does, and even if it had you would not write down the infinite decimals.
    Am I splitting hairs? Yes, in some cases. Many times, the data based on the measurement of the diameter can be takes as if it was continous, some times it can’t. What does it depends on? In the number of possible values that exist in the range of values. Example:
    5.2, 5.3, 5.2, 5.2, 5.2, 5.2, 5.3
    5,23, 5,26, 5.18, 5.24, 5.24, 5.31
    Do you see the difference? In the first case, it seems that there are just two possible values. In the second case there are 14 possible values. And if you increased even more the resolution of the data it will be closer and closer to being continous (of course it will never be).
    What happens with counts or ratios where the numerator is count? (number of defectives in the batch, number of calls per day, customer complaints…) They are discrete by nature. You cannot have 5.43 counts in one day. You will have either 5 or 6, with no possible value in the middle. Of course, if the data was allways discrete even if the variable was continous, it will remain discrete when the variable is already discrete. But, again, if you have enough possible values, continuity can be a good approach.
    So what’s your range of reasonably possible values in your calls per day count? Between 0 and 2? It is discrete. Between 199 and 201? It is discrete. Between 150 and 250? Well, it is still discrete, but can be taken as if it was continous.

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    #113506

    Thaly
    Member

    Ripley,
    Number of calls is discrete.
    Delivery time is continuous. Period.
    Like people said, you could try to fit your data and characterize them into a particular distribution.
    Thaly

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    #113511

    K.Subbiah
    Participant

    Hello Ripley:
    If you are interested in the number of calls per period and treat it as the random variable, it is of discrete nature; Always have per period or per person defined in your data. Typically, poisson distribution will be helpful in this circumstance. If the number of calls per period, for example, exceeds 10 (I think), then it will start resembling normal distribution. And we all know that normal distribution is used for RVs with continuous nature.
     
    If you are interested in the time between two calls (arrivals) and you treat it as your random variable, then it is of continuous nature; Exponential Dsitribution will be helpful here.
    Hope this helps. Good Luck.

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    #113512

    Solo
    Member

    Ripley,
    Believe it or not ;-) all data is, by defenition, discrete!  It is merely a matter of how precise the measurement system is. 
    How is being able to distinguish the difference between 0.00001 and 0.000001 any different than being able to distinguish the difference between 1,000,000 and 100,000? 
    Any data set could be made to be MORE continuous if you could just go one decimal place further to the right…
    My opinion:  Only if you could measure to an infinite number of decimal places would the data be truely continuous.
    -Solo

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    #113930

    Jonathon Andell
    Participant

    Good question.
    Officially, continuous data comes from a scale of measure that can be subdivided. Therefore, cycle time would be continuous, since a day can be divided into hours, then minutes, etc.
    Officially, one cannot subdivide a call to a call center, so it would not be continuous in the strictes sense. The time spent handling the call could be continuous.
    However, please refer back to Darth’s and others’ responses. If you get a volume of call that is high enough and variable enough, you can approximate the count as continuous data.

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    #113953

    Santosh Rayat
    Member

       HELLO : It is definitely a Discrete Data because the number of calls coming in is a whole Number. Therefore, it ca’t be continuous as there is no measurement of any kind at all.   Thanks a lot and looking forward to hearing from you soon.
    Regards,
    Santosh Rayat,
    905-846-9237
    [email protected]

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    #114477

    AC
    Participant

    Count means Discrete

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