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283.
The marks distribution of 30 students in a mathematics are given in the table. Find the mode of this data. Also compare and interpret the mode and mean.

Class interval

Number of students (f)

10-25

2

25-40

3

40-55

7

55-70

6

70-85

6

85-100

6

Case I: Finding Mode :
Here, the maximum class frequency is 7 and the class corresponding to frequency is 40 - 55. So the modal class is 40 - 55.

Thuse we have
Model class = 40.55
l = 40
f₁ = 7
f_{0 =}3
f₂= 6
and h = 15
Npw substituting these values in the formula of mode, we get

$Mode space equals space l italic space italic plus italic space open square brackets fraction numerator f subscript italic 1 italic minus f subscript italic 0 over denominator italic 2 f subscript italic 1 italic minus f subscript italic 0 italic minus f subscript italic 2 end fraction close square brackets italic cross times h italic space italic space italic space italic space italic space italic space italic space italic space italic equals italic space italic 40 italic plus open square brackets fraction numerator italic 7 italic minus italic 3 over denominator italic 2 italic cross times italic 7 italic minus italic 3 italic minus italic 6 end fraction close square brackets italic cross times italic 15 italic equals italic 40 italic plus open square brackets fraction numerator italic 4 over denominator italic 14 italic minus italic 9 end fraction close square brackets italic cross times italic 15 italic space italic space italic space italic space italic space italic space italic space italic space italic equals italic space italic 40 italic plus italic 4 over italic 5 italic cross times italic 15 italic equals italic 40 italic plus italic 12 italic equals italic 52$

Case II: Finding Mean

C.I.	f_i	x_i	d_i = x₂- 62.5	f_iu_i = d_i/h	f_iu_i
10-25	2	17.5	- 45	- 3	- 6
25-40	3	32.5	- 30	- 2	- 6
40-55	7	47.5	- 15	- 1	- 7
55-70	6	62.5 = A	0	0	0
70-85	6	77.5	15	1	6
85-100	6	92.5	30	2	12
	Σf_i = 30				Σf_iu_i= -1

top enclose straight x equals A plus fraction numerator begin display style sum from blank to blank of end style f subscript i u subscript i over denominator begin display style sum from blank to blank of end style f end fraction cross times h space space equals space 62.5 space plus open parentheses fraction numerator negative 1 over denominator 30 end fraction cross times 15 close parentheses space equals space 62.5 plus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses space equals space 62.5 minus 0.5 space equals space 62.

Hence, the mode of the given data is 52 while median is 62.
Interpretation : Maximum number of students obtained 52 marks, while on an average student obtained 62 marks.

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Short Answer Type

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

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

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

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

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283. The marks distribution of 30 students in a mathematics are given in the table. Find the mode of this data. Also compare and interpret the mode and mean. Class interval Number of students (f) 10-25 2 25-40 3 40-55 7 55-70 6 70-85 6 85-100 6

Short Answer Type

Long Answer Type

Short Answer Type

Long Answer Type

283.
The marks distribution of 30 students in a mathematics are given in the table. Find the mode of this data. Also compare and interpret the mode and mean.

Class interval

Number of students (f)

10-25

2

25-40

3

40-55

7

55-70

6

70-85

6

85-100

6