# a2-df.docx - Problem 1 a As we exploring descriptives in...

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Problem 1a.As we exploring descriptives in SPSS for age and fat percent with sample size n=18, we can clearly visualize that there seem to be two outliers on fat percent, in fact the median for fat percentage is 32.8, and all points are somewhat close to each other except 2 data points 8.8 and 10.5, distribution is also left-skewed. There is no outliers identified for age.b.Descriptive StatisticsNMinimumMaximumMeanStd. DeviationAge1826.0075.0050.111114.89923fatPercent188.8044.5031.06119.53977Valid N (listwise)18Difference between observed value and mean of sample divided by standard deviation of sample gives us z-score.Z=xμσOur statistical software does that for us, from descriptive we identify the mean and std.dev is 50.11 and 14.899, respectively. For fat percentage mean=31.06 and std.dev=9.54We can prove it solving by hand:
x=26 for age observed value, Z=2650.1114.89924.1114.899Z=-1.618c.Min-max normMin-max normalization performs the linear relationship on original data. The difference between observed value and minimum value dividedby the difference between max and min values.U=vxminxmaxxminRange [0,1] preserves relationship among original data points.Descriptive StatisticsNRangeMinimumMaximumMeanStd. Deviation
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