Question

FIND THE MEDIAN.
CLASS FREQUENCY
100-120 12
120-140 14
140-160 8
160-180 6
180-200 10​

Answer 1

Answer:

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

Step-by-step explanation: