SPSS Statistics

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Why doesn't a normal curve on histogram peak at the mode?

  • 1.  Why doesn't a normal curve on histogram peak at the mode?

    Posted 24 days ago
    I am new to SPSS and am still learning this tool and how it presents data. Just came across a confusing feature in the frequency analysis as below:

    1) Analyze menu -> Descriptive statistics -> Frequencies...
    2) In Frequencies window, select a scale variable to analyze.
    3) Click the Statistics... button, and select Histograms; and tick Show normal curve on histogram.

    The output is like the following, which can be changed with Binning to something to look nicer:

    histogram with normal curve
    histogram with normal curve
     Shouldn't the peak of normal curve coincide with the tallest bar which is the mode? I have asked around but no one seems to be able to explain why.


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    M K
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  • 2.  RE: Why doesn't a normal curve on histogram peak at the mode?

    Posted 24 days ago
    No, the normal distribution density function peaks at the mean.  Your data are decidedly nonnormal.

    If you want to explore what distributions might fit your data, try the Simulation procedure.

    Do Analyze > Simulation 
    Click Create Simulated Data and then Continue
    Click Create simulated data without a model
    Move the fields you are interested in to the Fields to be simulated box
    Click the Simulation tab at the top
    Click Fit All
    You will get information about the selected distribution, and you can click Fit Details to learn more.

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  • 3.  RE: Why doesn't a normal curve on histogram peak at the mode?

    Posted 24 days ago
    Thanks Jon. Now I realize the the normal curve overlay is a hypothetical normal curve used to compare the real data against a normal distribution. It sounded like a normal curve drawn from the real data. Thank you for the clarification!

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    M K
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  • 4.  RE: Why doesn't a normal curve on histogram peak at the mode?

    Posted 24 days ago
    It isn't hypothetical.  The mean and standard deviation are calculated from the data used for the frequencies, but the shape will always be a bell-shaped curve, because that is what the normal distribution is.  It just happens that with your data, that is a bad fit.  Your data are not normally distributed.
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  • 5.  RE: Why doesn't a normal curve on histogram peak at the mode?

    Posted 24 days ago
    Understood. Much appreciated for your explanation and help!