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Q1
The marks scored by 25 students in a test of 10 marks are given below:
1, 4, 5, 6, 0, 9, 3, 2, 3, 4, 6, 4, 5, 2, 7, 5, 2, 2, 3, 5, 1, 0, 7, 6, 3.
Taking classes as 0 – 2, 2 – 4, … etc., make a frequency table for the above distribution.Marks:2Answer:
The frequency distribution table for the given data is:

Q2
The weights in group of 50 oranges picked at random from a consignment are as follows: 131, 113, 82, 75, 204, 81, 84,1 18, 104, 110, 80, 107, 111, 114, 136, 123, 90, 78, 90, 115, 110, 98, 106, 99, 107, 84, 76, 186, 100, 109, 128, 115, 107, 115, 119, 93, 187, 139, 129, 130, 68, 195,123, 125, 111, 92, 86, 70, 126. Form the grouped frequency table by dividing the variable range into intervals of equal width, each corresponding to 20gms in such a way that the midvalue of the first class corresponding to 70gms.
Marks:3Answer:
We have,
Size of each class = 20
Midvalue of first class = 70
We know that if “a” is the midvalue of a class and h is the class size, then the lower and upper limits of the class are (a – h/2) and (a + h/2) respectively.
Here, a = 70 and h = 20
So, the lower limit of the first class interval = 70 – 10
= 60
And, the upper limit of the first class interval= 70 + 10
= 80
So, first class interval is 6080
Frequency Distribution of Weights of Oranges

Q3
The classmarks of a distribution are 26,31,36,41,46,51,56,61,66,71 find the true class limits.
Marks:3Answer:
Class size = difference between any two consecutive class marks
= 31 – 26
= 5
Lower class limit = 26 – 5/2
= 23.5
Upper Class limit = 26+5/2
= 28.5
These are the true class limits for 26.
Similarly we can calculate for others
Class Marks
Class Limits
26
23.528.5
31
28.533.5
36
33.538.5
41
38.543.5
46
43.548.5
51
48.553.5
56
53.558.5
61
58.563.5
66
63.568.5
71
68.573.5

Q4
The marks out of 100 of 70 students in a test are given below: 6 10 15 20 8 9 14 16 23 25 28 24 12 14 36 68 35 39 34 48 76 85 49 95 78 74 75 49 86 64 63 62 66 69 67 69 50 52 5 75 18 17 26 23 46 43 41 12 12 13 24 21 31 35 36 59 75 45 65 52 25 28 29 26 23 27 42 35 36 34
(i) Taking a class interval of size 10, construct a frequency as well as cumulative frequency table for the given data.
(ii) Which class has the largest frequency?
(iii) How many students score less than 40 marks?
(iv) How many students score first division (60% or more) marks?Marks:5Answer:
(i) The grouped frequency distribution table of the given data is:
Class intervals
Frequency
Cumulative frequency
0 – 10
4
4
10 – 20
11
15
20 – 30
15
30
30 – 40
10
40
40 – 50
8
48
50 – 60
4
52
60 – 70
9
61
70 – 80
6
67
80 – 90
2
69
90 – 100
1
70
(ii) Class interval 20 – 30 has the greatest frequency i.e., 15.
(iii) 40 students scored less than 40 marks.
(iv) 18 students scored first division marks. 
Q5
The electric bills of 50 houses is given below:
146 210 315 120 108 129
114 216 232 251 328 524
152 614 736 668 335 329
324 468 762 185 349 495
728 754 675 449 286 564
632 624 766 369 267 669
450 652 255 275 418 617
826 523 746 643 441 512
152 213
(i) Taking a class interval of size 50, construct a frequency as well as cumulative frequency table for the given data.
(ii) Which class has the largest frequency?Marks:5Answer:
(i) The grouped frequency distribution table of the given data is:
Class intervals
Frequency
Cumulative frequency
100 – 150
5
5
150 –200
3
8
200 –250
4
12
250 –300
5
17
300 –350
6
23
350 –400
1
24
400 –450
4
28
450 –500
2
30
500 –550
3
33
550 –600
1
34
600 –650
5
39
650 –700
4
43
700 –750
3
46
750 –800
3
49
800 –850
1
50
Total
50
(ii) 300 –350 has the largest frequency i.e., 6.