NORMAL DISTRIBUTION Normal curve Smooth, Bell shaped, bilaterally symmetrical curve Total area is =1 Mean is 0 Standard deviation=1 Mean, median, mode coincide. Area between X±1 SD=68.3% X±2SD=95.5% X±3SD=99.9%

Normal distribution

NORMAL DISTRIBUTION

POSITIVELY SKEWED

NEGATIVELY SKEWED

VARIABILITY Biological data are variable Two measurements in man are variable Cure rate are not equal but variable Height of students in same age group is not same but variable Height of students in one area is not same as compared to other place but variable Variability is essentially a normal character It is a biological phenomenon.

TYPES OF VARIABILITY Biological variability That occurs within certain accepted biological limits. It occurs by chance. –Individual variability –Periodical variability –Class, group or category variability –Sampling variability or sampling error

REAL VARIABILITY –When the difference between two readings or observations or values of classes or samples is more than the defined limits in the universe, it is said to be real variability. The cause is external factors. e.g. significant difference in cure rates may be due to a better drug but not due to a chance.

Experimental variability Errors or differences due to materials, methods, procedures employed in the study or defects in the techniques involved in the experiment. –Observer error –Instrumental error –Sampling error.

MEASURES OF VARIABILITY How individual observations are dispersed around the mean of a large series. Measures of variability of individual observations. –Range –Mean deviation –Standard deviation –Coefficient of variation

Measures of variability of sample –Standard error of mean –Standard error of difference between two means –Standard error of proportion –Standard error of difference between two proportions –Standard error of correlation coefficient –Standard error of regression coefficient.

RANGE Range defines the normal limits of a biological characteristic. It is the simplest measure of dispersion Usually employed as a measure of variability in medical practice It indicates the distance between the lowest and highest. It ignores all observations except two extreme values on which it is based. Normal range covers observations falling in 95% confidence limits.

examples Observ. Range Mean SD Age mrge Menst.cycle Pulse rate Wt. at birth Syst.BP

MEAN DEVIATION It the average of the deviations from the arithmetic mean. M.D=∑ (X-¯X) n Example: 83,75,81,79,71,90,75,95,77,94.

MEAN DEVIATION D BPMeanDeviation from mean=X-X M.D=5.6

STANDARD DEVIATION Most frequently used measure of deviation “Root – means—square--deviation” –Calculate the mean –Find the difference of each observation from the mean –Square the differences of observations from the mean –Add the squared values to get sum of squares –Divide this sum by number of observations to get mean –squared deviation, called variance –Find the square root of this variance to get root mean squared deviation.

USES OF S.D. 1. Summarizes the deviations of a large distribution from mean in one figure used as a unit of variation 2. Indicates whether the variation of difference of an individual from the mean is by chance i.e. natural or real i.e. defines the limits of variability 3. Helps in finding standard error which determines whether the difference b/w means of two similar samples is by chance or real. 4. Find suitable size of sample

SD Calculate SD from following weights of students. 40,45,50,55,60,65,70,75,80 Mean = 540/ 9=60 Kg Calculate mean from every observation

SD WeightMeanWt-mean(Wt-Mean)²

COEFFICIENT OF VARIATION Used to compare relative variability Used to compare variability of one of one character into two groups having different magnitude of values CV= SD X 100 mean

CV PersonsMean HtSD Adults160Cm10Cm Children60 Cm 5 Cm CV of adults=10/160 X 100=6.25% CV of children = 5/60 X 100=8.33%

SD M= (M)195SD=5

SD