Page 210 - Data Science class 10
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2
                                                     2
                                  2
                                                 2
                                         2
                                             2
                                      2
                                                            2
                          2

                                                         2
                              2
                      2
               =  6 +4 +4 +3 +3 +2 +1 +1 +1 +1 +3 +6 +11         2
                                        13
















               =  36 + 16 + 16 + 9 + 9 + 4 + 1 + 1 + 1 + 1 + 9 + 36 + 121
                                       13
               =   260
                  13
               = 20
               Hence, the population variance is 20.
          10.  Find the sample variance of the following dataset:
               5, 8, 11, 3, 2, 10, 9, 11, 12, 3, 12, 18, 24, 26
          Ans.  Find the mean by adding all data values and divide by the sample size n.
                       (5 + 8 + 11 + 3 + 2 + 10 + 9 + 11 + 12 + 3 + 12 + 18 + 24 + 26)
               Mean =
                                                   14
                    = 11
               The sample variance is:
                                                        ∑ n  x  – x ) 2
                                                    8 8   i= 1 ( 1
                                                            n  –1

                                                          2
                                                                 2
                                           2

                                                  2



                                                                                 2




                                                                                        2


                                                                                                2
                            2
                                                                         2

                                    2
                     2

                                                                                                        2
               =  (5–11) +(8–11) +(11–11) +(3–11) +(2–11) +(10–11) +(9–11) +(11–11) +(12–11) +(3–11) +(12–11) +(18–11) +(24–11) 2
                                                              13 – 1
                              2
                                                         2
                      2
                                                             2
                          2
                                                      2
                                          2
                                                                  2

                                      2
                                              2
                  2

                                  2
                                                  2
               =  6 + 3 + 0 + 8 + 9 + 1 + 2 + 0 + 1 + 8 + 1 + 7 + 13 + 15 2
                                           13

















               =  36 + 9 + 64 + 81 + 1 + 4 + 1 + 64 + 1 + 49 + 169 + 225
                                       13
               =   704
                  13
               = 54.153846
               Hence, the population variance is 54.153846.
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