Question

Case study: ( 17 to 20): 4 questions
17. The students of class 10 were given different activities. One group was given the activity
to record the weights of the students of class and submit a grouped data to the teacher.
After working for 5 days students submitted the following data. Answer the questions
based on the submitted data.
10
Weight (in kg) Number of
students
40-44
4
44-48
6
48-52
10
52-56
14
56-60
60-64
8
64-68
6
68 - 72
2
1. What is the modal class of the given data?
a) 48-52 ; b) 52-56;
c) 56 - 60; d) 40 - 44
2. What is the median class of the data?
a) 52-56; b) 48-52; c) 60-64; d) None of the above
3. The model weight lie in which class?
a) 60-64; b) 44-48; c) 52-56; d) 68-72
4. What will be the cumulative frequency of the class 60 - 64?
a) 56;
b) 68;
c) 52;
d) 60​

Answer 1

Given:

We are provided with a grouped data of class having a record of the weights of the students of class 10.

Weight (in kg)   Number of students

40-44                         4

44-48                         6

48-52                        10

52-56                        14

56-60                        10

60-64                         8

64-68                         6

68-72                         2

To find :

1. What is the modal class of the given data ?

2. What is the median class of the data ?

3. The modal weight lie in which class ?

4. What will be the cumulative frequency of the class 60-64 ?

Step-by-step explanation:

       1. The modal class is the class with the highest frequency i.e.

        in the given the data 52-56 is the modal class with highest no. of

        students i.e., 14.

      Option (b) is the correct answer.  

    2. Weight (in kg)    Number of students         Cumulative frequency

            40-44                         4                                         4

            44-48                         6                                         10

            48-52                        10                                        20

            52-56                        14                                        34

            56-60                        10                                        44

            60-64                         8                                        52

            64-68                         6                                        58

            68-72                         2                                        60

                                             N = 60

        Median class is observed by cumulative frequency.

        Cumulative frequency is calculated by adding frequency with the

        succeeding frequency.

       1st  c.f. will be same as 1st frequency.

       2nd c.f. will be 1st c.f. + 2nd frequency and so on.

       Median class is observed by  locating cumulative frequency which is           greater than or equal to  $\frac{N}{2}$.

        where N = Total of Frequency

               $\frac{N}{2}=\frac{60}{2}=30$

       So the cumulative frequency more than 30 is 34 of  class 52-56.

      Option (a) is the correct answer.

3. To calculate modal weight  we have to find the mode first

             $l + \frac {{f_{1}} -{f_{0}}} {{2f_{1}}-{f_{0}}-{f_{2}}} \times h$

    where $l$ = lower limit of the modal class

               ${f_{1}}$ = frequency of the modal class

               ${f_{0}}$ = frequency of the class preceding the modal class

               ${f_{2}}$ = frequency of the class succeeding the modal class

               $h$ = class size

$l = 52, {f_{1}} = 14, {f_{2}} = 10, {f_{3}} = 10, h = 4$

                $52+\frac{14-10}{2\times14-10-10}}\times4$

                $52+\frac{4}{8}\times4$

               $52+2$

              Mode = $54$

 So the modal weight lies in class 52-56.

Option (c) is the correct answer

4. The  cumulative frequency of the class 60-64 is 52.

 Option (c) is the correct answer.

 

     

   

                     

Answer 2

Answer:

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