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Statistic formulas for class 8th, 9th, 10th, Calculation of mean, mode, median, mean deviation about mean & median, standard deviation, variance.
CI 
\[x_{i}\] 
\[f_{i}\] 
\[f_{i}x_{i}\] 
     
     
     
     


\[\sum f_{i}\] 
\[\sum f_{i}x_{i}\] 
CI 
\[x_{i}\] 
\[f_{i}\] 
\[u_{i}=\frac{x_{i}a}{h}\] 
\[f_{i}u_{i}\] 
     
     
     
     
     


\[\sum f_{i}\] 

\[\sum f_{i}u_{i}\] 
CI 
\[f_{i}\] 
cf 
    
    
    

\[\sum f_{i}\] 

Measures of Dispersion:
There are following measures of Dispersion:
i) Range, ii) Quartile Deviation, iii) Mean Deviation iv) Standard Deviation
In this chapter we will study all measures except Quartile Deviation.
Range : Maximum Value  Minimum value
Mean Deviation:\[Mean \: of \: Deviations=\frac{Sum\: of\: deviations}{Number\: of\: Deviations}\]In this chapter we discuss two types of Mean Deviation.
i) Mean Deviation about mean ii) Mean Deviation about Median
CI 
\[x_{i}\] 
\[f_{i}\] 
\[\left x_{i}\bar{x} \right \] 
\[f_{i}\left x_{i}\bar{x} \right
\] 
    
    
    
    
    


\[\sum f_{i}\] 

\[\sum f_{i}\left
x_{i}\bar{x} \right \] 
CI 
\[x_{i}\] 
\[f_{i}\] 
\[\left x_{i}M
\right \] 
\[f_{i}\left
x_{i}M \right \] 
    
    
    
    
    
\[\sum f_{i}\] 
\[\sum f_{i}\left x_{i}M \right \] 
Note: For calculating mean class interval may or may not be continuous. But for calculating median class intervals should be continuous.LimitationsWhile calculating Mean deviation about mean and about median we take absolute values and ignore the negative sign. So this calculation is not become very scientific. Also in many cases it gives unsatisfactory results.This imply that we need another measure of Dispersion. Standard Deviation is such a measure of central tendency.Variance and Standard Deviation.While calculating mean deviation about mean or median, the absolute values of the deviations were taken otherwise deviations may cancel among themselves.Another way to overcome this difficulty which arose due to the sign of deviations, is to take square of all the deviations. Mean of squares of deviations about mean is called Variance.
CI 
\[x_{i}\] 
\[f_{i}\] 
\[y_{i}=\frac{x_{i}a}{h}\] 
\[f_{i}y_{i}\] 
\[f_{i}y_{i}^{2}\] 
    
    
    
    
    
    


\[\sum f_{i}\] 

\[\sum f_{i}y_{i}\] 
\[\sum f_{i}y_{i}^{2}\] 
\[Standard Deviation (S.D.) = \sqrt{Variance},\; It\; is \; \; denoted \; \; by\; \; "\sigma "\]
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