I've been in a debate with my graduate-level statistics professor about "normal distributions". I contend that to truly get a normal distribution one must have mean=median=mode, all the data must be contained under the bell curve, and perfectly symmetrical around the mean. Therefore, technically, there are virtually NO normal distributions in real studies, and we should call them something else, perhaps "near-normal". 

She says I'm too picky, and if the skew/kurtosis are less than 1.0 it is a normal distribution and took off points on an exam. The dataset is total number of falls/year in a random sampling of 52 nursing homes which is a random sample of a larger population. Any insight?

**Problem:**

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> QUESTION: 3. Compute measures of skewness and kurtosis for this data. Include a histogram with a normal curve. Discuss your findings. Is the data normally distributed? 
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> ```
> Statistics 
> Number of falls  
> N  Valid    52
>    Missing   0
> Mean        11.23
> Median      11.50
> Mode         4a
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> ```
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> a. Multiple modes exist. The smallest value is shown
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> ```
> Number of falls  
> N  Valid    52
>    Missing   0
> Skewness      .114
> Std. Error of Skewness    .330
> Kurtosis  -.961
> Std. Error of Kurtosis    .650
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> ```
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**My answer:**

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> The data is platykurtic and has only slight positive skewing, and it is NOT a normal distribution because the mean and median and mode are not equal and the data is not evenly distributed around the mean. In reality virtually no data is ever a perfect normal distribution, although we can discuss “approximately normal distributions” such as height, weight, temperature, or length of adult ring finger in large population groups.
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**Professor's answer:**

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> You are correct that there is no perfectly normal distribution. But, we are not looking for perfection. We need to look at data in addition to the histogram and the measures of central tendency. What do the skewness and kurtosis statistics tell you about the distribution? Because they are both between the critical values of -1 and +1, this data is considered to be normally distributed.
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