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WORLD OF AVERAGES


     Let us take 60 samples of 10 students each(total 600 students).   For each sample, we calculate a average mark in a particular subject.  We get the following reports.


         MARKS RANGE                                        NO.AVERAGES IN THE RANGE        
        30.0--44.0                                                                        5
        44.1--58.0                                                                        13
        58.1--72.0                                                                        23
        72.1--86.0                                                                        12
        86.1--100                                                                          6  
                                                                                              ----------
        maximum  marks:150                                                        60        total no. averages or samples
                                                                                              ----------
                                                         
     Let us draw a bar graph for the above data.  We get a curve as shown in figure 1.
     This curve is called normal distribution curve or bell curve.  The averages of sample data (heights and weights of people, BP levels) always yield a normal curve.  This concept is also called central limit theorem.





     If we increase the size of the samples and number of samples, we will get smooth normal curve as shown in figure 2.


     Inferences from the curve:  The peak of the curve indicates most probable average or universal average.

      The curve tells that the probability of observing a particular data value is greatest near the mean value- (the universal average) and fades away  rapidly as the difference from the mean increases.  The curve also indicates that the occurrence of extreme values is so rare.  That is, very short person, highly intelligent person is so rare.

 Applications:  Many real world data, for example; weights of chicken, memory power, cholesterol values, employee job satisfaction, returns from share investments etc,.Mostly follow normal distribution.  So normal curve can be drawn for these data and decisions can be made based on the curve.

 Science update:  Vaccines saved one corer lives and prevented 450 corer cases.

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