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# Standard deviation

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### Standard deviation

1. 1. M.Prasad Naidu MSc Medical Biochemistry, Ph.D,.
2. 2.  It is an improvement over mean deviation  Measure of dispersion  Used most commonly in statistical analyses
3. 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. 4.  If large sample size :  If sample less than 30 : Square root of variance that gives SD
5. 5. For ex : Mean = 2+5+3+4+1/5 = 15/5 = 3 Var = 10/5 = 2
6. 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. 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
8. 8. 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
9. 9. 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
10. 10.  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.