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STANDARD DEVIATION

RESEARCH METHODOLOGY

mprasadnaidu
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STANDARD DEVIATION

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  1. STANDARD DEVIATION 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. Square root of variance that gives SD • If large sample size : • If sample less than 30 :

  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. SD of normal curve • 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”

  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. Thank you

  10. 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

  11. 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.

  12. THANK YOU

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