Question

Find the median class less than 120 140 160 180 200 frequency 12 26 34 40 50

Answer 1

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

$Class Frequency</p><p>f </p><p>i</p><p> </p><p> Midvalue</p><p>x </p><p>i</p><p> </p><p> f </p><p>i</p><p> </p><p> x </p><p>i</p><p> </p><p> cf </p><p> 100−200 12 110 1320 12 </p><p>120−140 14 130 1820 26 </p><p>140−160 8 150 1200 34 </p><p>160−180 6 170 1020 40 </p><p>180−200 10 190 1900 50 </p><p> ∑f </p><p>i</p><p> </p><p> =50 ∑f </p><p>i</p><p> </p><p> x </p><p>i</p><p> </p><p> =7260 </p><p>⇒ Mean= </p><p>f </p><p>i</p><p> </p><p> </p><p>∑f </p><p>i</p><p> </p><p> x </p><p>i</p><p> </p><p> </p><p> </p><p> = </p><p>50</p><p>7260</p><p> </p><p> =145.2</p><p></p><p>⇒ We have, N=50. Then, </p><p>2</p><p>N</p><p> </p><p> =25.</p><p>⇒ Median class is 120−140</p><p></p><p>l= lower limit of the modal class</p><p>h= size of the class intervals</p><p></p><p>f= frequency of the modal class</p><p></p><p>f </p><p>1</p><p> </p><p> = frequency of the class preceding the modal class</p><p></p><p>f </p><p>2</p><p> </p><p> = frequency of the class succeed in the modal class.</p><p></p><p></p><p>⇒ So, l=120,h=20,N=50cf=12,f=14.</p><p></p><p>Median=l+ </p><p>f</p><p>2</p><p>N</p><p> </p><p> −cf</p><p> </p><p> ×h</p><p></p><p>⇒ Median=120+ </p><p>14</p><p>25−12</p><p> </p><p> ×20</p><p></p><p>⇒ Median=120+ </p><p>7</p><p>130</p><p> </p><p> </p><p></p><p>∴ Median=120+18.6=138.6</p><p></p><p>⇒ Modal class =120−140</p><p></p><p>⇒ l=120,f=14f </p><p>1</p><p> </p><p> =12,f </p><p>2</p><p> </p><p> =8,h=20</p><p></p><p>⇒ Mode=l+ </p><p>2f−f </p><p>1</p><p> </p><p> −f </p><p>2</p><p> </p><p> </p><p>f−f </p><p>1</p><p> </p><p> </p><p> </p><p> ×h</p><p></p><p>⇒ Mode=120+ </p><p>2×14−12−8</p><p>14−12</p><p> </p><p> ×20</p><p></p><p>⇒ Mode=120+ </p><p>8</p><p>40</p><p> </p><p> </p><p></p><p>∴ Mode=125$

×h

⇒ Mode=120+

2×14−12−8

14−12

×20

⇒ Mode=120+

8

40

∴ Mode=125