M.Prasad NaiduMSc Medical Biochemistry,

Ph.D,.

It is an improvement over mean deviation

Measure of dispersion

Used most commonly in statistical analyses

Calculation of SDFirst find the mean of seriesFind the deviation or difference of

individual measurement from meanNext find the sum of squares of deviation

or difference of individual measurements from their mean

Now find the variance (Var) – mean squared deviation

var = ∑ (X - X) 2/ n

If large sample size :

If sample less than 30 :

Square root of variance that gives SD

For ex :

Mean = 2+5+3+4+1/5 = 15/5 = 3

Var = 10/5 = 2

Uses of SDIt summarizes the deviation of a large distribution from mean in one figure used as unit of variation

Indicates whether the variation of difference of an individual from mean is by chance

Helps in finding the SE which determines whether the difference between means of two similar samples is by chance or real

Helps in finding the suitable size of sample for valid conclusion.

The shape of curve will depend upon mean and SD of which in turn depend upon the number and nature of observation.

In normal curve :-Area b/w 1 SD on either side of mean will

include approximately 68% of values in distribution

Area b/w 2 SD is 95%Area b/w 3 SD is 99.7%These limits on either side of mean are called

“confidence limits”

SD of normal curve

Standard normal curveSmoothbell shapedPerfectly symmetricalBased on infinity large number of

observationTotal area of curve = 1Mean = 0 SD = 1Mean , median and mode all coincide

SD of normal curve Bell shaped curve will show an inflexion on the ascending as well as descending units of curve

If vertical lines are drawn from each of these points they will intersect the X axis on either side of the mean at an equal distance from it

A large portion of area under the normal curve has been included in portion of curve b/w the 2 points of inflexion

The distance b/w the mean and point of inflexion either side is equal to SD and is denoted by a + sign prefixed to it to indicate that it extends on either side of mean.

If another vertical line is drawn an either side of mean at a distance equal to twice SD most of values in distribution table would have been included in this part of curve

In most cases, + SD will include 2/3 of sample values and mean + 2 SD will include 90% of values.