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5.   Explain the relationship between variance and mean of a data set.
                     Ans.  The variance represents how far the data in your sample are grouped around the mean. Data sets with low variance
                          have data grouped closely about the mean. Data sets with high variance have data grouped far from the mean.

                     6.   What are frequency bins in the context of the frequency domain?

                     Ans.  Frequency bins are the intervals between samples in the frequency domain. For example, with a sample rate of 100
                          Hz and an FFT size of 100, the 100 Hz range would be divided into 100 intervals, each representing a frequency bin.

                 B.   Long answer type questions.

                     1.   If    9 − 1  0   = A +    1  2  − 1   then find the matrix A.
                            − 2 1  3      0  4  6 
                     Ans.  Given matrix equation can be rewritten as:

                                                   1
                              9  −1  0   1  2  − 
                          A
                          A= =           −        
                              −2  1  3    0  4  6 
                          Subtracting the individual elements
                             91     − −    01
                                              + 
                                      12
                               −
                                              + 
                                      12
                               −
                          A =  91   − −    01  
                             
                          A =  −−    1  − 4  36   
                                              −
                               20
                             
                                              −
                              −−20   1 − 4  36 
                            8  −3 1 
                          =   8  −3 1  
                           
                                3
                            
                               −−3
                                3
                          = −2  −−3    
                            −2
                           
                     2.   If A =    2 4   and B =     1 3   then find A – B.
                                6 2         − 4 5 
                                       24          1   3
                     Ans.  Given,  A =      and B=    
                                        62         −45 
                                      24     1  3
                                  −
                          ∴      AB=        −     
                                       62    −45 
                                                  − 
                                      21       43
                                         −
                                     =             
                                         −−4)
                                                  −
                                       6 (     25  
                                      1   1 
                                     =     
                                       10  −3 
                                                      2  −1      1
                                                      
                     3.   Find the inverse of the matrix  A = 1  1  1   .
                                                      
                                                       1  1      2 
                                                      
                     Ans.  |A| = 2(2-1) – (-1) (2-1) + 1(1-1)
                             2+1+0 = 3
                          |A| = 3
                                   1  3  − 2               1     1  3  − 2  
                                            
                          Adj A =      −  1  3 −  1                  A  =    A –1 =  − 1  3  −  1  3 −  1 
                                            
                                     0 − 3  3                  0 − 3  3   
                     4.   Find the mean, median and mode of the following data.
                              Class        0-10         10-20        20-30       30-40        40-50         Total
                            Frequency       16            8           35           36           5           100

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