Standard Deviation Explained and Visualized

have we discovered new particle in physics is manufacturing process out of control what percentage of men are taller than LeBron James how about taller than Yao Ming all these questions can be answered using the concept of standard deviation for any set of data the mean and standard deviation can be calculated for example five people may have the following amounts of money in their wallets 21 50 6285 and $90 the mean is $61.60 and the standard deviation is $281 how much does the data vary from the average standard deviation is measure of spread that is how spread out set of data is low standard deviation tells us that the data is closely clustered around the mean or average while high standard deviation indicates that the data is dispersed over wider range of values standard deviation is used when the distribution of data is approximately normal resembling bell curve standard deviation is commonly used to understand whether specific data point is standard and expected or unusual and unexpected standard deviation is represented by the lowercase Greek letter Sigma data Point's distance from the mean can be measured by the number of standard deviations that it is above or below the mean data point that is beyond certain number of standard deviations from the mean represents an outcome that is significantly above or below the average this can be used to determine whether result is statistically significant or part of expected variation such as whether bottle with an extra ounce of soda is to be expected or warrants further investigation into the production line the 6895 99.7 rule tells us that about 68% of the data fall within one standard deviation of the mean about 95% of data fall within two standard deviations of the mean and about 99.7% of data fall within three standard deviations of the mean the average height of an American adult male is 510 with standard deviation of 3 in using the 6895 99.7 rule this means that 68% of American men are 510 plus or minus 3 in 95% of American men are 510 plus orus 6 in and 9 99.7% of American men are 510 plus orus 9 in so this means only about 3% of American men deviate more than 9 in from the average with 0.15% taller than 67 and 0.1 5% shorter than 51 this reasoning suggests that LeBron James is 1 in 2,500 and Yao Ming is 1 in 450 million in particle physics scientists have what are called 5 Sigma results results that are five standard deviations above or below the mean result that varies this much can signify discovery as it has only 1 in 3.5 million chance that it is due to random fluctuation in summary standard deviation is measure of spread along with the mean the standard deviation allows us to determine whether this value is statistically significant or part of expected variation thanks for watching see you next time cre using pun