Question

compute mean median mode for the following data
mark- 0-10 10-20 20-30 30-40 40-50 50-60
number of student 8 23 45 65 75 80
respectively
very important pls with steps and I will
mark brainly​

Answer 1

Answer:

Median and mean values of the marks obtained by the students of a class are 46.67 and 45.5 respectively. Find out mode of the marks. Answer: Given, Median (M ) = ...

Answer 2

Answer:

Mean = 28, Median = 27.73. Mode = 27.19

Step-by-step explanation:

Given:  

   Mark          : 0-10 10-20 20-30 30-40 40-50 50-60

 Number of students:    8     23       45      65        75       80

To find: Mean, median, mode.

Solution: The number of students represents the cumulative frequency. So we need to find the frequency from c.f.

  Mark     $x_{i}$           frequency  cumulative Frequency     $f_{i*x_{i} }$              

 0-10      10/2=5            8                        8                             5×8=40

10-20     30/2=15       23-8=15                23                           15×15=225  

20-30    50/2=25      45-23=22             45                           25×22=550

30-40     70/2=35      65-45=20             65                         35×20=700      

40-50     90/2=45     75-65=10               75                          45×10=450          

50-60    110/2=55     80-75=5               80                         55×5=275          

                                 N=Σ$f_{i}$=80                                               Σ$f_{i}x_{i}$=2240

Mean:

Mean= Σ $(f_{i}x_{i})$/Σ$f_{i}$ ,

where $x_{i}$ is the class mark and $x_{i}$ = (upper limit +lower limit)/2

           $f_{i}$ is the frequency of the class interval.

Mean = 2240/80 = 28.

Median:

To find median we have to find cumulative frequency ,n/2 and median class.

Median = l + $\frac{(\frac{n}{2} -cf)}{f}$ × h,

where  cf- cumulative frequency of the class preceding the median class

             l- lower limit of the median class

             f- frequency of the median class

             h- width of median class or class size

             n -  number of observations.

           Median class = class whose cumulative frequency is greater than (nearest to) n/2.

Here n/2=80/2=40, c.f. greater than n/2=40 is 45.

So median class =20-30,l=20, f=22  , h= 10,cf= 23.

 Median =20+(40-23) ×10

                            22

              = 20+(17×10)/22

             =20+170/22

             =20+7.73

Median =27.73        

Mode :

We can use the relation between mean, median and mode to find mode if the other two values are known.

3 Median = Mode + 2 mean

3×27.73 = Mode + 2 × 28

83.19= Mode + 56

Mode = 83.19-56 = 27.19

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