Question 1: Arrange the following data in ascending order:

(i) 8, 3, 11, 15, 1, 7, 16, 25, 9, 4

(ii) 5.7, 9.2, 3.1, 4.6, 1.8, 10.4, 2.5, 0.9, 1.2

Answer:

(i) 1, 2, 4, 7, 8, 9, 11, 15, 16, 25

(ii) 0.9, 1.2, 1.8, 2.5, 3.1, 4.6, 5.7, 9.2, 10.4

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Question 2: Arrange the following data in descending order:

(i) 15, 3, 0, 11, 7, 2, 23, 14, 29, 5, 1, 7

(ii) 2.3, 4.6, 1.2, 0.4, 3.5, 9.7, 6.1, 4.8, 0.8, 1.0

Answer:

(i) 29, 23, 17, 15, 14, 11, 7, 5, 3, 2, 1, 0

(ii) 9.7, 6.1, 4.8, 4.6, 3.5, 2.3, 1.2, 1.0, 0.8, 0.4

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Question 3: Construct a frequency table for each of the following data:

(i) 3, 2, 5, 4, 1, 3, 2, 2, 5, 3, 1, 2, 1, 1, 2, 2, 3, 4, 5, 3, 1, 2, 3

(ii) 7, 8, 6, 5, 6, 7, 7, 9, 8, 10, 7, 6, 7, 8, 8, 9, 10, 5, 7, 8, 7, 6

(iii) 152, 165, 172, 144, 135, 156, 175, 140, 132, 150, 153, 147

(iv) 13, 25, 19, 16, 8, 30, 27, 6, 0, 34, 40, 11, 4 , 17

Answer:

(i) First step is to arrange the data in ascending order.

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3

x Tally f
1  Tally Marks 5
2  Tally Marks {\mid  \mid } 7
3  Tally Marks {\mid  } 6
4  {\mid  \mid } 2
5  {\mid  \mid \mid } 3

(ii) First step is to arrange the data in ascending order.

5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8 , 9, 9, 10, 10

x Tally f
5 {\mid  \mid } 2
6 4
7 Tally Marks {\mid  \mid } 7
8 Tally Marks 5
9 {\mid  \mid } 2
10 {\mid  \mid } 2

(iii) First step is to arrange the data in ascending order.

132, 135, 140, 144, 147, 150, 152, 153, 156, 165, 172, 175

Class Interval Tally f
130-135 {\mid } 1
135-140 {\mid } 1
140-145 {\mid  \mid } 2
145-150 {\mid } 1
150-155 {\mid  \mid \mid } 3
155-160 {\mid } 1
160-165 0
165-170 {\mid } 1
170-175 {\mid } 1
175-180 {\mid } 1

(iv) First step is to arrange the data in ascending order.

0, 4, 6, 8, 11, 13, 16, 17, 19, 25, 27, 30, 34, 40

x Tally f
0-10 {\mid  \mid \mid \mid} 4
10-20 Tally Marks 5
20-30 {\mid  \mid } 2
30-40 {\mid  \mid } 2
40-50 {\mid } 1

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Question 4: Fill in the blanks:

(i) Lower limit of the class interval 14-22 is \underline{14} .

(ii) Upper limit of the class interval 16-25 is \underline{25} .

(iii) Class size of the interval 20-30 is \underline{10} .

(iv) If the upper and the lower limits of a class interval be 18 and 11 respectively, then the class interval is \underline{11-18}

(v) If the lower and the upper limit of the class interval be 11.5 and 21.5 respectively, then the class interval is \underline{11.5 - 21.5} .

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Question 5: The marks out of 50 , obtained by 30 students of a class in an examination are given below:

40, 12, 46, 37, 17, 27, 30, 6, 2, 23, 19, 39, 25, 5, 33

19, 21, 12, 41, 17, 12, 19, 17, 8, 10, 1, 9, 21, 13, 48

Arrange them in ascending order and present it in a grouped data, by taking class interval as 0-10, 10-20, 20-30, 30-40, 40-50

Answer:

In ascending order: 1, 2, 5, 6, 8, 9, 10, 12, 12 , 12 , 13, 17, 17, 17, 19, 19, 19, 21, 21, \\ 23, 25, 2730, 33, 37, 39, 40, 41, 46, 48

x

f (number of students)

0-10

6

10-20

11

20-30

5

30-40

4

40-50

4

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Question 6: The fine imposed in Rs. on 40 students for being absent is given below:

18, 8, 12, 6, 8, 16, 12, 5, 23, 2, 16, 23, 2, 10, 20, 12, 9, 7, 0, 5,

3, 6, 27, 21, 19, 15, 20, 24, 2, 16, 14, 8, 23, 24, 10, 14, 3, 8, 11, 2

Present the data in the form of frequency distribution table by taking class interval of 0-5, 5-10, 10-15, 15-20, 20-25 .

Answer:

Fine (Rs.) Tally f (no of students)
0-5 Tally Marks {\mid  \mid } 7
5-10 Tally Marks Tally Marks 10
10-15 Tally Marks {\mid  \mid \mid } 8
15-20 Tally Marks{\mid } 6
20-25 Tally Marks {\mid  \mid \mid } 8
25-30 {\mid } 1

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Question 7: The weight in kg of 30 students are given below:

48, 55, 30, 43, 41, 36, 48, 37, 34,,38, 46, 42, 38, 52, 37,

34, 40, 42, 50, 37, 35, 46, 42, 45, 43, 37, 39, 45, 48, 46

For the group frequency table by taking class intervals 30-35, 35-40, 40-45, 45-50, 50-55 .

Answer:

Weight (kgs) Tally f (no of students)
30-35 {\mid  \mid \mid } 3
35-40 Tally Marks {\mid  \mid \mid \mid} 9
40-45 Tally Marks {\mid  \mid } 7
45-50 Tally Marks {\mid  \mid \mid } 8
50-55 {\mid  \mid \mid } 3

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Question 8: The daily income in Rs of 30 workers is given below:

83, 96, 91, 80, 97, 111, 90, 83, 112, 120, 103, 77, 82, 90, 70,

68, 89, 85, 78, 105, 94, 97, 90, 89, 102, 113, 90, 106, 70, 84

Construct a frequency table using groups 65-75, 75-85, 85-95, 95-105, 105-115, 115-125 .

Answer:

Class Interval Tally f
65-75 {\mid  \mid \mid } 3
75-85 Tally Marks {\mid  \mid } 7
85-95 Tally Marks {\mid  \mid \mid \mid} 9
95-10 Tally Marks 5
105-115 Tally Marks 5
115-125 {\mid } 1

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Question 9: The heights of 45 students measured to the nearest centimeter are given below:

155, 166, 159, 161, 158, 154, 153, 159, 157, 152, 160, 157, 158, 170,

152, 151, 162, 164, 171, 154, 165, 161, 150, 168, 162, 154, 160, 170, 163, 164, 

165, 169, 165, 155, 157, 158, 160, 161, 156, 153, 150, 165, 167, 169, 172

Prepare a frequency table taking class intervals 150-155, 155-160, 160-165, 165-170, 170-175

Answer:

Class Interval Tally f
150-155 Tally Marks Tally Marks 10
155-160 Tally Marks Tally Marks {\mid } 11
160-165 Tally Marks Tally Marks {\mid } 11
165-170 Tally Marks {\mid  \mid \mid \mid} 9
170-175 {\mid  \mid \mid \mid} 4

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Question 10: Complete the table:

Answer:

Class Interval Class Limit Class Size Class Mark Class Boundaries
Lower Upper Lower Upper
25-30 25 30 5 27.5 25 30
30-35 30 35 5 32.5 30 35
35-40 35 40 5 37.5 35 40
40-45 40 45 5 42.5 40 45

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Question 11: Complete the table

Answer:

Class Interval Class Limit Class Size Class Mark Class Boundaries
Lower Upper Lower Upper
26-30 26 30 5 28 25.5 30.5
31-35 31 35 5 33 30.5 35.5
36-40 36 40 5 38 35.5 40.5
41-45 41 45 5 43 40.5 45.5

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