Question

21. The following table show the weight (in gms) of a sample of 100 apples, taken from a
large consignment. Find the median weight of apples.
Weight(in gms) 50-60 60-70 70-80 80-90 90-100 100-110 110-120 120-130
No. of apples
8
10 12 16 18
12
10​

Answer 1

Step-by-step explanation:

b)it is 10,12,16,18

hope this helps

Answer 2

Correct Question:

The following table shows the weight (in gms) of a sample of 100 apples, taken from a large consignment. Find the median weight of apples.

Weight(in gms): 50-60 60-70 70-80 80-90 90-100 100-110 110-120 120-130

No. of apples 8 10 12 16 18 24 12 10​

⇒The median weight of apples is 92.22 gms

Step-by-step explanation:

Given:

Weight(in gms):

50-60  60-70  70-80  80-90  90-100  100-110  110-120  120-130

No. of apples:

8  10  12  16  18   24  12  10

To find:

Median weight of apples

Solution:

We calculate the cumulative frequencies(c.f.) using the frequencies given as no. of apples

The c.f. for the first class will be the same as 8

The c.f. for the class 60-70 will be 8+10= 18

The c.f. for the class 70-80 will be 18+12= 30

      c.f. for the class 80-90 will be 30+16=46

       c.f. for the class 90-100 will be 46+18=64

       c.f. for the class 100-110 will be 64+24=78

       c.f. for the class 110-120 will be 78+12= 90

       c.f. for the class 80-90 will be 90+10= 100

Now the value of N is 100

∴ N\2= 100\2

        = 50th term

The closest and greater than c.f. to the 50th term is 64

So, the corresponding class 90-100 will be the median class.

Median= $l+\frac{\frac{N}{2}-c.f. }{f} h$

where $l$= lower limit of the median class=90

         $\frac{N}{2}$= 50

        $c.f.$= cumulative frequency of the class preceding median class=46

       $f$=frequency of the median class= 18

      $h$= difference between upper limit and limit of the median class

       = 100-90=10

Putting all the values in formula

Median= $l+\frac{\frac{N}{2}-c.f. }{f} h$

Median= $90+\frac{50-46 }{18} 10$

∴ Median= $90+\frac{4}{18} (10)$

               = $90+\frac{40}{18}$

              = $90+2.22$

∴ Median= $92.22$ gms

Thus, the median weight of apples is 92.22gms