Question

Find the mode of the following distribution of marks obtained by a student
marks obtained = 0-20 ,20-40,40-60,60-80,80-100
no of stidients 15,18,21,29,17
if the mean of the above distribution in 53 using empiral relationship estimate the value of its mode​

Answer 1

Answer:

20. 40. 60 these are the mode of the following

Answer 2

Answer:

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STATISTICS

Find the mode of the following distribution of marks obtained by the students in an examination:

Marks obtained 0−20 20−40 40−60 60−80 80−100

Number of students 15 18 21 29 17

Given the mean of the above distribution is 53, using empirical relationship estimate the value of its median.

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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