Question

5-7, 7-9, 9-11,11-13, 13-15,15-17,17-19. frequency 20 ,18,22,15,20,15,10​

Answer 1

to find mean I use direct  method

Step-by-step explanation:first we need to find class mark(xi)

herclass mark( xi) can be find by adding lower limit and upper limit and dividing by 2

class interval     frequency(fi)        classmark (xi)            fixi

5-7                         20                     5+7=12/2=6                120

7-9                          18                     7+9=16/2=8                  144

9-11                         22                  9+11=20/2=10                220

11-13                        15                   11+13=24/2`=12               180

13-15                       20                      14                                280

15-17                       15                         16                                 240

17-19                       10                           18                               180

total                    120                                                            1360

 mean(x-) = fixi/xi

                = 1360/120

                =11.3

to find mode  

formula =l+(f1-f0/2f1-f0-f2)h

we need to find model class

take the class inverval which has highest frequency

•  here the model class is 9-11 which has frequency 22

• the model class frequency is taken as f1 and f2 is taken has the next frequency and f0 is taken as the frequency before f1  

      h is taken as the difference between the class interval

       model class =9-11 ,here  l can be taken as 9 because it is the first digit in model class

        fi=22

        f0=18

        f2=15

       h=2

     mode=l+(f1-f0/2fi-f0-f2)h

              = 9+(22-18/2 multiply22-18-15)2

             = 103/11=9.3