What is standard deviation in statistics ? pls explain me with a realtime example?

Answer 1

The standard deviation measure sthe spread of the data. If you have a mean of a given value x and the distribution of the variable is normal you can conclude that if you move on standard deviation away from the maen in both direction then the area under the graph is roughly 2/3. Ie: there is a 66.6% chance that if you add all the samples of data that are withinthat range they will make up 66.6% of the sample data. There is a 66% cahance of falling in that range


Example
50 people are interveiwd and their height measure. The average height is 5meters
the Standard deviation squared= variance= [1/(n-1)] [sum of x^2 - [(sum of x)^2/n] ]

x= the heights
n= sample size
sum of x^2= square all the x values and add them together


If you construct a distribution function and the standard deviation turns out to be two then
1) 66% of all the people where between 7 and 3 meters tall
2) there is a 66% chance (in this sample) of being 7-3 meters tall
3) the area below the graph with 7 and 3 as the upper and lower bounds =0.66.6

Answer 2

Standard deviation is the most widely used measure of the spread of data. An example might be the heights of adult men. The mean is something like 70 inches and the standard deviation about 3 inches. From this, and assuming a normal distribution of heights, you can work what proportion are over 6 feet or under 5' 6" etc. If in some country the mean is 70 inches and the s.d. 2 inches then the men in that country are on average the same height as the rest of the world but much more close to the average with fewer very tall or very short.

Answer 3

if you have a population with a parameter P , it has two chararteristics

first the mean : if n is the frequency of the population

mean = (p1+p2+....pn)/n usually this value is written p with a bar on the p. here I write it as Pm

standard deviation
std = (((p1-Pm)^2 +(p2-Pm)^2 +..(pn-Pm))^2/(n-1))^1/2


example 5 values 16, 18, 20, 22, 24

Pm = 16+18+20+22+24/5 =100/5 =20

std = (((16-20)^2+(18-20)^2+(20-20)^2+(22-20)^2+(24-20)^2/(5-1)^^0.5

calculate
std = (16+4+0+4+16)^0.5 = 40^0.5 = 6.32

std =