Page 208 - Data Science class 10
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Ans.  Sorting the data in ascending order
                 Wages

                   100
                   200
                   300
                   500
                   600

               The number elements are 5. So the median is:
                          51 +  th
               Median =       th element
                          2  
                      = 3rd element
                      = 300
            5.  Following are the marks of some students in a periodic test:

                Marks   6  8   8  6  7   5  4  9   5  7  4   9  8  3   2  6  9  3   5  6  8   6  4  7   3  7  6
               Find the mode from the above dataset.

          Ans.  Arrange the marks in ascending order

                Marks   2  3   3  3  4   4  4  5   5  5  6   6  6  6   6  6  7  7   7  7  8   8  8  8   9  9  9
               Notice that 6 occurred 6 times. So mode is 6.
            6.  Find the Standard Deviation of the following series:

               10, 8, 10, 8, 8, 4
          Ans.  The formula for Standard Deviation is as follows:

                                   ∑  n  x  – x ) 2
               Standar Deviation =    i= 1  ( 1
                                       n  –1
               Calculating the mean
                       (10 + 8 + 10 + 8 + 8 + 4)  48
               Mean =                          =      = 8
                                  6               6
               Hence,    x    = 8
                          ̅
                         n= 6

               Then,

                                     (10 –8 ) (8 –8+  2  ) (10 –8+  2  ) (8 –8+  2  ) (8 –8+  2  ) ( 4 –8+  2  ) 2
               Standard Deviation =
                                                             6 –1

                                     ( ) ( ) ( ) ( ) ( ) ( ) 4+  2  2  0  2  +  2 +  2  0  2  +  0  2  +  2
                                 =
                                                   6 –1

                                 =   24
                                     5

                                 =   4.8
                                 = 2.19
               Standard Deviation is 2.19.
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