MATHEMATICS [3 marks sum]

Following data gives the number of children in 40 families :
1,2,6,5,1,3,2,6,2,3,4,2,0,4,4,3,2,2,0,0,1,2,2,4,4,3,2,1,0,5,1,2,4,3,4,1,1,6,2,2
Represent it in the form of a frequency distribution.

Convert the following frequency distribution to exclusive form :

Class-interval	Frequency
30-34	7
35-39	9
40-44	13
45-49	6
50-54	3
55-59	10

Use this table to find:
(i) The true class-limits of the fourth class-interval
(ii) The class-boundaries of the fifth class-interval
(iii) The class-mark of the third class-interval
(iv) The class-size of the sixth class-interval.

Construct a frequency table from the following data :

Age (in years)	Number of students
Less than 10	6
Less than 20	14
Less than 30	30
Less than 40	52
Less than 50	65
Less than 60	70

Construct a frequency distribution table from the following cumulative frequency distribution :

Class-interval	Cumulative frequency
0 - 8	8
8 - 16	21
16 - 24	26
24 - 32	33
32 - 40	42

Construct the cumulative frequency table from the frequency table given below :

Class-interval	0-6	6-12	12-18	18-24	24-30
Frequency	7	11	8	14	12

Construct a frequency table for the following ages (in years) of 30 students using equal class-intervals, one of them being 9 - 12, where 12 is not included.
18,12,7,6,11,15,21,9,8,13,15,17,22,19,14,21,23,8,12,17,15,6,18,23,22,16,9,21,11,16

The marks obtained by 35 students in an examination are given below :
370, 290, 318, 175, 170, 410, 378, 405, 380, 375, 315, 305, 325, 275, 241, 288, 261, 355, 402, 380, 178, 253, 428, 240, 210, 175, 154, 405, 380, 370, 306, 460, 328, 440, 425
From a cumulative frequency table with class intervals of length 50.

Construct a frequency table for the following ages (in years) of 30 students using equal class-intervals, one of them being 9 - 12, where 12 is not included.
18, 12, 7, 6, 11, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12, 17, 15, 6, 18, 23, 22, 16, 9, 21, 11, 16

Following data gives the number of children in 40 families :
1, 2, 6, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 1, 6, 2, 2
Represent it in the form of a frequency distribution.

The class marks of a frequency distribution are 28, 34, 40, 46, 52. Find the class-size and all the class-intervals.