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284.
The following table shows the marks obtained by 100 students of class X in a school during a particular academic session. Find the mode of this distribution.

Marks

No. of students

Less than 10

7

Less than 20

21

Less than 30

34

Less than 40

46

Less than 50

66

Less than 60

77

Less than 70

92

Less than 80

100

Class Marks (C.I.)	No. of students (c.f.)	f
Less than 10	7	7
Less than 20	21	14
Less than 30	34	13
Less than 40	46	12
Less than 50	66	20
Less than 60	77	11
Less than 70	92	15
Less than 80	100	8

The class (40-50) has maximum frequency i.e. 20 therefore, modal class is 40-50.
f = 20
Now, l = 40, h = 10m, f₁= 20 and f₂= 11
f₀= 12 and modal class = 40 - 50

$therefore space Mode space equals space l space plus space fraction numerator straight f subscript 1 minus straight f subscript 0 over denominator 2 straight f subscript 1 minus straight f subscript 0 minus straight f subscript 2 end fraction cross times straight h rightwards double arrow space space space Mode space equals space 40 plus fraction numerator 20 minus 12 over denominator 2 left parenthesis 20 right parenthesis minus 12 minus 11 end fraction cross times 10 rightwards double arrow space space Mode space equals space space 40 plus fraction numerator 8 over denominator 40 minus 12 minus 11 end fraction straight x 10 rightwards double arrow space space Mode space equals space 40 plus 8 over 17 cross times 10 rightwards double arrow space Mode space equals space 40 plus 8 over 17 rightwards double arrow space Mode space equals space 40 plus 4.70 rightwards double arrow space Mode space equals space 44.70$

3134 Views

285.

Calculate the median of the following distribution of incomes of employees of a company.

Income	No. of Persons
400-500	25
500-600	69
600-700	107
700-800	170
800-900	201
900-1000	142
1000-1100	64

361 Views

Long Answer Type

286.

Find the mean, mode and median for the following data :

Class	0-10	10-20	20-30	30-40	40-50	Total
Frequency	8	16	36	34	6	100

388 Views

Short Answer Type

287.

The median of the following data is 52.5. Find the values of x and y if the total frequency is 100.

Class Interval	Frequency
0-10	2
10-20	5
20-30	x
30-40	12
40-50	17
50-60	20
60-70	y
70-80	9
80-90	7
90-100	4
	Total 100

1979 Views

288.

Calculate the median from the following data:

Value	Frequency
Less than 10	4
Less than 20	16
Less than 30	40
Less than 40	76
Less than 50	96
Lc9s than 60	112
Less than 70	120
Less than 80	125

1819 Views

289.

Calculate the median from the following data:

Size	Frequency
More than 50	0
More than 40	40
More than 30	98
More than 20	123
More than 10	165

193 Views

Long Answer Type

290.

The median of the following data is 20.75. Find the missing frequencies x and y, if the total frequency is 100.

Class Interval	0 - 5	5 - 10	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35	35 - 40
Frequency	7	10	x	13	y	10	14	9

7298 Views

Class	Frequcncy
10-15	3
15-20	2
20-25	10
25-30	7
30-35	20
35-40	5
40-45	8

Class interval	Number of students (f)
10-25	2
25-40	3
40-55	7
55-70	6
70-85	6
85-100	6

Murks (C.I.)	No. of students (f)
0-10	5
10-20	12
20-30	14
30-40	10
40-50	8
50-60	6

Marks	No. of students
Less than 10	7
Less than 20	21
Less than 30	34
Less than 40	46
Less than 50	66
Less than 60	77
Less than 70	92
Less than 80	100