The Gaussian distribution also called as normal distribution is the most important probability distribution in statistics. As it fits in different area such as pressure, weight , height error measurement etc. natural phenomena this distribution.
The distribution follows 68–95–99 rule . What is this ??
assuming μ as median value in bell curve its first standard deviation lies are 68%, 2nd are 95 and third are 99.7%.
Standard Normal Distribution and Standard Scores
The name itself denotes as standard which says the values are standard. The mean value is 0 and standard deviation is 1. It is also called as Z-distribution. And similarly the value in such distribution is called as z-score.
Standardization :: How to calculate standard scores
Z = (x-μ ) /σ
where, σ is Standard deviation and μ is mean
Example of comparing the apple and oranges
suppose we have following data
fruit >> >>>>>>>> — — — Apples — — — — Orange
mean weight grams >> — — — -100 — — — — —140
standard deviation >> — — — — 15 — — — — — — 25
apple weigh 110 gm and orange 100 gm
Calculating the z-scores
apple = (110–100)/15 = 0.667
orange = (100–140)/25 =-1.6
The +ve z-score means apple weighs more than average apple . Similarly, orange with -ve means below the mean weight for oranges.