Question

12. Find the inode of the following distribution of marks obtained fo
by students in an examination
0-20
20-40
40-60
60-80
80-100
Marks
obtained
No. of
students
15
18.
21
29
17​

Answer 1

Answer:

Marks obtained Number of students

0−20 15

20−40 18

40−60 21

60−80 29

80−100 17

Here,

modal class : 60−80

lower limit of the modal class l=60

h= size of class interval =20

f

0

= frequency of the class just before the modal class =21

f

1

= frequency of the modal class =29

f

2

= frequency of the class just after the modal class =17

Mode =l+

2f

1

−f

0

−f

2

f

1

−f

0

×h=60+

58−21−17

29−21

×20=60+

20

160

=68

∴ Mode, Mean =53

Mean, median and mode are related by the following empirical relationship :

Mean- Mode =3 ( Mean- Median)

OR

3-Median =2× Mean+Mode

∴ Median =

3

Mode+2×Mean

=

3

68+2×53

=59

∴ Median =59