Question

find the mean ,median and mode of the following data
CI: 100-120,120-140,140-160,160-180,180200
f:12,14,8,6,10​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

Class Frequency

f  

i

​

  Midvalue

x  

i

​

  f  

i

​

x  

i

​

  cf  

100−200 12  110  1320  12  

120−140  14  130  1820  26  

140−160  8  150  1200  34  

160−180 6  170  1020 40  

180−200  10  190  1900  50  

 ∑f  

i

​

=50   ∑f  

i

​

x  

i

​

=7260  

⇒  Mean=  

f  

i

​

 

∑f  

i

​

x  

i

​

 

​

=  

50

7260

​

=145.2

⇒  We have, N=50. Then,  

2

N

​

=25.

⇒  Median class is 120−140

l= lower limit of the modal class

h= size of the class intervals

f= frequency of the modal class

f  

1

​

= frequency of the class preceding the modal class

f  

2

​

= frequency of the class succeed in the modal class.

⇒  So, l=120,h=20,N=50cf=12,f=14.

Median=l+  

f

2

N

​

−cf

​

×h

⇒  Median=120+  

14

25−12

​

×20

⇒  Median=120+  

7

130

​

 

∴   Median=120+18.6=138.6

⇒  Modal class =120−140

⇒  l=120,f=14f  

1

​

=12,f  

2

​

=8,h=20

⇒  Mode=l+  

2f−f  

1

​

−f  

2

​

 

f−f  

1

​

 

​

×h

⇒  Mode=120+  

2×14−12−8

14−12

​

×20

⇒  Mode=120+  

8

40

​

 

∴  Mode=125