This document discusses standard deviation (SD), which is a measure of dispersion used commonly in statistical analysis. It describes how to calculate SD by finding the mean, deviations from the mean, sum of squared deviations, and variance. For large samples, the square root of the variance gives the SD. SD summarizes how much values vary from the mean, helps determine if differences are due to chance, and indicates appropriate sample sizes. For a normal distribution, about 68% of values fall within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD.

1. M.Prasad Naidu
MSc Medical Biochemistry, Ph.D,.

2.  It is an improvement over mean deviation
 Measure of dispersion
 Used most commonly in statistical analyses

3. Calculation of SD
 First find the mean of series
 Find the deviation or difference of individual
measurement from mean
 Next 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

4.  If large sample size :
 If sample less than 30 :
Square root of variance that gives SD

5. For ex :
Mean = 2+5+3+4+1/5 = 15/5 = 3
Var = 10/5 = 2

6. Uses of SD It 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.

7.  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

9. Standard normal curve
 Smooth
 bell shaped
 Perfectly symmetrical
 Based on infinity large number of observation
 Total area of curve = 1
 Mean = 0
 SD = 1
 Mean , median and mode all coincide

14. 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

15.  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.