EvanJ | January 25th, 2017 06:47 PM | How Close To The Normal Distribution Is My Data? I have 351 numbers. About half are on each side of the mean. 169 are higher than the mean and 182 are lower than the mean. Here is how my data compares to the normal distribution in terms of what percent of the numbers are within 0.5, 1, and 2 standard deviations of the mean:
Within 0.5 standard deviations: exactly 1/3rd of my numbers, 38.3% for the normal distribution
Within 1 standard deviation: 63.5% of my numbers, 68.3% for the normal distribution
Within 2 standard deviations: 97.2% of my numbers, 95.4% for the normal distribution
The farthest from the mean any of my numbers are is 2.5334 standard deviations above the mean, so all of my numbers are within 3 standard deviations of the mean. It's obvious that my numbers are less likely than the normal distribution to be within 1 standard deviation of the mean and more likely than the normal distribution to be between 1 and 2 standard deviations away from the mean. The highest 35 numbers (about 10 percent of 351) are an average of 1.728 standard deviations above the mean. The lowest 35 numbers are an average of 1.598 standard deviations below the mean.
Without looking at all the numbers, would you say the numbers are close to being normally distributed? |