Page 1 Question:1 The number of members in 20 families are given below: 4, 6, 5, 5, 4, 6, 3, 3, 5, 5, 3, 5, 4, 4, 6, 7, 3, 5, 5, 7. Prepare a frequency distribution of the data. Solution: First, we will arrange the data in increasing order. 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7 Frequency table of the above data: Number of members Tally marks Number of families f r e q u e n c y 3 | | | | 4 4 | | | | 4 5 | | | | || 7 6 | | | 3 7 || 2 Total 20 Question:2 A dice was thrown 30 times and the following outcomes were noted: 2, 1, 2, 4, 6, 1, 2, 3, 6, 5, 4, 4, 3, 1, 1, 3, 1, 1, 5, 6, 6, 2, 2, 3, 4, 2, 5, 5, 6, 4. Prepare a frequency table. Solution: Arranging the outcomes in increasing order, we get: 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6 Now, we have: 1 was thrown 6 times 2 was thrown 6 times 3 was thrown 4 times 4 was thrown 5 times 5 was thrown 4 times 6 was thrown 5 times Frequency distribution table of the above data: Number Tally mark frequency 1 | | | | | 6 2 | | | | | 6 3 | | | | 4 4 | | | | 5 5 | | | | 4 6 | | | | 5 Total 30 Page 2 Question:1 The number of members in 20 families are given below: 4, 6, 5, 5, 4, 6, 3, 3, 5, 5, 3, 5, 4, 4, 6, 7, 3, 5, 5, 7. Prepare a frequency distribution of the data. Solution: First, we will arrange the data in increasing order. 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7 Frequency table of the above data: Number of members Tally marks Number of families f r e q u e n c y 3 | | | | 4 4 | | | | 4 5 | | | | || 7 6 | | | 3 7 || 2 Total 20 Question:2 A dice was thrown 30 times and the following outcomes were noted: 2, 1, 2, 4, 6, 1, 2, 3, 6, 5, 4, 4, 3, 1, 1, 3, 1, 1, 5, 6, 6, 2, 2, 3, 4, 2, 5, 5, 6, 4. Prepare a frequency table. Solution: Arranging the outcomes in increasing order, we get: 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6 Now, we have: 1 was thrown 6 times 2 was thrown 6 times 3 was thrown 4 times 4 was thrown 5 times 5 was thrown 4 times 6 was thrown 5 times Frequency distribution table of the above data: Number Tally mark frequency 1 | | | | | 6 2 | | | | | 6 3 | | | | 4 4 | | | | 5 5 | | | | 4 6 | | | | 5 Total 30 Marks Tally marks Frequency 0-10 ||| 3 10-20 |||| ||| 8 20-30 |||| |||| |||| 14 30-40 |||| |||| 9 40-50 |||| | 6 Total 40 Question:3 The following data gives the number of children in 40 families: 1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2. Represent it in the form of a frequency distribution. Solution: Arranging the dates in ascending order, we get: 0, 0 ,0 , 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2,2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6 There are: 4 families with no children 7 families with 1 child 12 families with 2 children 5 families with 3 children 6 families with 4 children 3 families with 5 children 3 families with 6 children The frequency distribution table for the above data can be generated as below: Number of children Tally mark Number of families f r e q u e n c y 0 | | | | 4 1 | | | | | | 7 2 | | | | | | | | | | 12 3 | | | | 5 4 | | | | | 6 5 | | | 3 6 | | | 3 Total 40 Question:4 The marks obtained by 40 students of a class in an examination are given below: 8, 47, 22, 31, 17, 13, 38, 26, 3, 34, 29, 11, 22, 7, 15, 24, 38, 31, 21, 35, 42, 24, 45, 23, 21, 27, 29, 49, 25, 48, 21, 15, 18, 27, 19, 45, 14, 34, 37, 34. Prepare a frequency distribution table with equal class intervals, starting from 0-10 w h e r e10 n o t i n c l u d e d . Solution: Arranging the given observations in ascending order, we get: 3, 7, 8, 11, 13, 14, 15, 15, 17, 18, 19, 21, 21, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 29, 29, 31, 31, 34, 34, 34, 35, 37, 38, 38, 42, 45, 45, 47, 48, 49 Thus, the frequency distribution may be represented as shown below: Question:5 The electricity bills i n r u p e e s of 25 houses of a certain locality for a month are given below: 324, 700, 617, 400, 356, 365, 435, 506, 548, 736, 780, 378, 570, 685, 312, 630, 584, 674, 754, 776, 596, 745, 565, 763, 472. Arrange the above data in increasing order and form a frequency table using equal class intervals, starting from 300-400, where 400 is not included. Page 3 Question:1 The number of members in 20 families are given below: 4, 6, 5, 5, 4, 6, 3, 3, 5, 5, 3, 5, 4, 4, 6, 7, 3, 5, 5, 7. Prepare a frequency distribution of the data. Solution: First, we will arrange the data in increasing order. 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7 Frequency table of the above data: Number of members Tally marks Number of families f r e q u e n c y 3 | | | | 4 4 | | | | 4 5 | | | | || 7 6 | | | 3 7 || 2 Total 20 Question:2 A dice was thrown 30 times and the following outcomes were noted: 2, 1, 2, 4, 6, 1, 2, 3, 6, 5, 4, 4, 3, 1, 1, 3, 1, 1, 5, 6, 6, 2, 2, 3, 4, 2, 5, 5, 6, 4. Prepare a frequency table. Solution: Arranging the outcomes in increasing order, we get: 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6 Now, we have: 1 was thrown 6 times 2 was thrown 6 times 3 was thrown 4 times 4 was thrown 5 times 5 was thrown 4 times 6 was thrown 5 times Frequency distribution table of the above data: Number Tally mark frequency 1 | | | | | 6 2 | | | | | 6 3 | | | | 4 4 | | | | 5 5 | | | | 4 6 | | | | 5 Total 30 Marks Tally marks Frequency 0-10 ||| 3 10-20 |||| ||| 8 20-30 |||| |||| |||| 14 30-40 |||| |||| 9 40-50 |||| | 6 Total 40 Question:3 The following data gives the number of children in 40 families: 1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2. Represent it in the form of a frequency distribution. Solution: Arranging the dates in ascending order, we get: 0, 0 ,0 , 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2,2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6 There are: 4 families with no children 7 families with 1 child 12 families with 2 children 5 families with 3 children 6 families with 4 children 3 families with 5 children 3 families with 6 children The frequency distribution table for the above data can be generated as below: Number of children Tally mark Number of families f r e q u e n c y 0 | | | | 4 1 | | | | | | 7 2 | | | | | | | | | | 12 3 | | | | 5 4 | | | | | 6 5 | | | 3 6 | | | 3 Total 40 Question:4 The marks obtained by 40 students of a class in an examination are given below: 8, 47, 22, 31, 17, 13, 38, 26, 3, 34, 29, 11, 22, 7, 15, 24, 38, 31, 21, 35, 42, 24, 45, 23, 21, 27, 29, 49, 25, 48, 21, 15, 18, 27, 19, 45, 14, 34, 37, 34. Prepare a frequency distribution table with equal class intervals, starting from 0-10 w h e r e10 n o t i n c l u d e d . Solution: Arranging the given observations in ascending order, we get: 3, 7, 8, 11, 13, 14, 15, 15, 17, 18, 19, 21, 21, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 29, 29, 31, 31, 34, 34, 34, 35, 37, 38, 38, 42, 45, 45, 47, 48, 49 Thus, the frequency distribution may be represented as shown below: Question:5 The electricity bills i n r u p e e s of 25 houses of a certain locality for a month are given below: 324, 700, 617, 400, 356, 365, 435, 506, 548, 736, 780, 378, 570, 685, 312, 630, 584, 674, 754, 776, 596, 745, 565, 763, 472. Arrange the above data in increasing order and form a frequency table using equal class intervals, starting from 300-400, where 400 is not included. Electricity bills i n R u p e e s Tally marks Frequency 300-400 |||| 5 400-500 ||| 3 500-600 |||| | 6 600-700 |||| 4 700-800 |||| || 7 Total 25 Weekly wages i n R u p e e s Tally marks Frequency 610-630 |||| 4 630-650 |||| 4 650-670 |||| 5 670-690 ||| 3 690-710 |||| || 7 710-730 |||| 5 Total 28 Weekly pocket expenses i n R u p e e s Tally marks Frequency 60-70 |||| | 6 70-80 |||| 5 80-90 |||| || 7 90-100 |||| 5 100-110 ||| 3 110-120 |||| 4 Total 30 Solution: Arranging the given observations in increasing order, we get: 312, 324, 356, 365, 378, 400, 435, 472, 506, 548, 565, 570, 584, 596, 617, 630, 674, 685, 700, 736, 745, 754, 763, 776, 786 Thus, the frequency distribution may be represented as shown below: Question:6 The weekly wages i n r u p e e s of 28 workers of a factory are given below: 668, 610, 642, 658, 668, 620, 719, 720, 700, 690, 710, 642, 672, 654, 692, 706, 718, 702, 704, 678, 615, 640, 680, 716, 705, 615, 636, 656. Construct a frequency table with equal class intervals, taking the first of the class intervals as 610-630, where 630 is not included. Solution: Arranging the given observations in ascending order, we get: 610, 615, 615, 620, 636, 640, 642, 642, 654, 656, 658, 668, 668, 672, 678, 680, 690, 692, 700, 702, 704, 705, 706, 710, 716, 718, 719, 720 Thus, the frequency distribution may be represented as shown below: Question:7 The weekly pocket expenses i n r u p e e s of 30 students of a class are given below: 62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103, 96, 64, 94, 87, 85, 105, 115. Construct a frequency table with class intervals 60-70 w h e r e70 i s n o t i n c l u d e d , 70-80, 80-90, etc. Solution: Arranging the given observations in increasing order, we get: 60, 62, 62, 64, 65, 68, 72, 72, 73, 75, 78, 80, 80, 84, 85, 86, 87, 87, 90, 94, 94, 95, 96, 100, 103, 105, 110, 115, 117, 118 Thus, the frequency distribution may be represented as given below: Question:8 The daily earnings i n r u p e e s of 24 stores in a market was recorded as under: 715, 650, 685, 550, 573, 530, 610, 525, 742, 680, 736, 524, 500, 585, 723, 545, 532, 560, 580, 545, 625, 630, 645, 700. Prepare a frequency table taking equal class sizes. One such class is 500-550, where 550 is not included. Solution: Arranging the given observations in increasing order, we get: 500, 524, 525, 530, 532, 545, 545, 550, 560, 573, 580, 585, 610, 625, 630, 645, 650, 680, 685, 700, 715, 723, 736, 742 Thus, the frequency distribution may be represented as given below: Page 4 Question:1 The number of members in 20 families are given below: 4, 6, 5, 5, 4, 6, 3, 3, 5, 5, 3, 5, 4, 4, 6, 7, 3, 5, 5, 7. Prepare a frequency distribution of the data. Solution: First, we will arrange the data in increasing order. 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7 Frequency table of the above data: Number of members Tally marks Number of families f r e q u e n c y 3 | | | | 4 4 | | | | 4 5 | | | | || 7 6 | | | 3 7 || 2 Total 20 Question:2 A dice was thrown 30 times and the following outcomes were noted: 2, 1, 2, 4, 6, 1, 2, 3, 6, 5, 4, 4, 3, 1, 1, 3, 1, 1, 5, 6, 6, 2, 2, 3, 4, 2, 5, 5, 6, 4. Prepare a frequency table. Solution: Arranging the outcomes in increasing order, we get: 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6 Now, we have: 1 was thrown 6 times 2 was thrown 6 times 3 was thrown 4 times 4 was thrown 5 times 5 was thrown 4 times 6 was thrown 5 times Frequency distribution table of the above data: Number Tally mark frequency 1 | | | | | 6 2 | | | | | 6 3 | | | | 4 4 | | | | 5 5 | | | | 4 6 | | | | 5 Total 30 Marks Tally marks Frequency 0-10 ||| 3 10-20 |||| ||| 8 20-30 |||| |||| |||| 14 30-40 |||| |||| 9 40-50 |||| | 6 Total 40 Question:3 The following data gives the number of children in 40 families: 1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2. Represent it in the form of a frequency distribution. Solution: Arranging the dates in ascending order, we get: 0, 0 ,0 , 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2,2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6 There are: 4 families with no children 7 families with 1 child 12 families with 2 children 5 families with 3 children 6 families with 4 children 3 families with 5 children 3 families with 6 children The frequency distribution table for the above data can be generated as below: Number of children Tally mark Number of families f r e q u e n c y 0 | | | | 4 1 | | | | | | 7 2 | | | | | | | | | | 12 3 | | | | 5 4 | | | | | 6 5 | | | 3 6 | | | 3 Total 40 Question:4 The marks obtained by 40 students of a class in an examination are given below: 8, 47, 22, 31, 17, 13, 38, 26, 3, 34, 29, 11, 22, 7, 15, 24, 38, 31, 21, 35, 42, 24, 45, 23, 21, 27, 29, 49, 25, 48, 21, 15, 18, 27, 19, 45, 14, 34, 37, 34. Prepare a frequency distribution table with equal class intervals, starting from 0-10 w h e r e10 n o t i n c l u d e d . Solution: Arranging the given observations in ascending order, we get: 3, 7, 8, 11, 13, 14, 15, 15, 17, 18, 19, 21, 21, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 29, 29, 31, 31, 34, 34, 34, 35, 37, 38, 38, 42, 45, 45, 47, 48, 49 Thus, the frequency distribution may be represented as shown below: Question:5 The electricity bills i n r u p e e s of 25 houses of a certain locality for a month are given below: 324, 700, 617, 400, 356, 365, 435, 506, 548, 736, 780, 378, 570, 685, 312, 630, 584, 674, 754, 776, 596, 745, 565, 763, 472. Arrange the above data in increasing order and form a frequency table using equal class intervals, starting from 300-400, where 400 is not included. Electricity bills i n R u p e e s Tally marks Frequency 300-400 |||| 5 400-500 ||| 3 500-600 |||| | 6 600-700 |||| 4 700-800 |||| || 7 Total 25 Weekly wages i n R u p e e s Tally marks Frequency 610-630 |||| 4 630-650 |||| 4 650-670 |||| 5 670-690 ||| 3 690-710 |||| || 7 710-730 |||| 5 Total 28 Weekly pocket expenses i n R u p e e s Tally marks Frequency 60-70 |||| | 6 70-80 |||| 5 80-90 |||| || 7 90-100 |||| 5 100-110 ||| 3 110-120 |||| 4 Total 30 Solution: Arranging the given observations in increasing order, we get: 312, 324, 356, 365, 378, 400, 435, 472, 506, 548, 565, 570, 584, 596, 617, 630, 674, 685, 700, 736, 745, 754, 763, 776, 786 Thus, the frequency distribution may be represented as shown below: Question:6 The weekly wages i n r u p e e s of 28 workers of a factory are given below: 668, 610, 642, 658, 668, 620, 719, 720, 700, 690, 710, 642, 672, 654, 692, 706, 718, 702, 704, 678, 615, 640, 680, 716, 705, 615, 636, 656. Construct a frequency table with equal class intervals, taking the first of the class intervals as 610-630, where 630 is not included. Solution: Arranging the given observations in ascending order, we get: 610, 615, 615, 620, 636, 640, 642, 642, 654, 656, 658, 668, 668, 672, 678, 680, 690, 692, 700, 702, 704, 705, 706, 710, 716, 718, 719, 720 Thus, the frequency distribution may be represented as shown below: Question:7 The weekly pocket expenses i n r u p e e s of 30 students of a class are given below: 62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103, 96, 64, 94, 87, 85, 105, 115. Construct a frequency table with class intervals 60-70 w h e r e70 i s n o t i n c l u d e d , 70-80, 80-90, etc. Solution: Arranging the given observations in increasing order, we get: 60, 62, 62, 64, 65, 68, 72, 72, 73, 75, 78, 80, 80, 84, 85, 86, 87, 87, 90, 94, 94, 95, 96, 100, 103, 105, 110, 115, 117, 118 Thus, the frequency distribution may be represented as given below: Question:8 The daily earnings i n r u p e e s of 24 stores in a market was recorded as under: 715, 650, 685, 550, 573, 530, 610, 525, 742, 680, 736, 524, 500, 585, 723, 545, 532, 560, 580, 545, 625, 630, 645, 700. Prepare a frequency table taking equal class sizes. One such class is 500-550, where 550 is not included. Solution: Arranging the given observations in increasing order, we get: 500, 524, 525, 530, 532, 545, 545, 550, 560, 573, 580, 585, 610, 625, 630, 645, 650, 680, 685, 700, 715, 723, 736, 742 Thus, the frequency distribution may be represented as given below: Daily earnings i n R u p e e s Tally marks Frequency 500-550 ||||| || 7 550-600 ||||| 5 600-650 |||| 4 650-700 ||| 3 700-750 ||||| 5 Total 24 Heights i n c m Tally marks Frequency 125-130 |||| 5 130-135 |||| || 7 135-140 |||| | 6 140-145 |||| 4 Total 22 Question:9 The heights i n c m of 22 students were recorded as under: 125, 132, 138, 144, 142, 136, 134, 125, 135, 130, 126, 132, 135, 142, 143, 128, 126, 136, 135, 130, 130, 133. Prepare a frequency distribution table, taking equal class intervals and starting from 125-130, where 130 is not included. Solution: Arranging the given observations in increasing order, we get 125, 125, 126, 126, 128, 130, 130, 130, 132, 132, 133, 134, 135, 135, 135, 136, 136, 138, 142, 142, 143 and 144. Thus, the frequency distribution may be represented as given below: Question:10 The top speeds of 30 different land animals have been organised into a frequency table given below: Maximum speed i n k m/ h 10–20 20– 30 30– 40 40– 50 50– 60 60– 70 Number of animals 3 5 10 8 0 2 Draw a histogram for the given data. Solution: Question:11 The ages i n y e a r s of 360 patients treated in a hospital on a particular day are given below: Age i n y e a r s 10– 20 20– 30 30– 40 40– 50 50– 60 60– 70 Page 5 Question:1 The number of members in 20 families are given below: 4, 6, 5, 5, 4, 6, 3, 3, 5, 5, 3, 5, 4, 4, 6, 7, 3, 5, 5, 7. Prepare a frequency distribution of the data. Solution: First, we will arrange the data in increasing order. 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7 Frequency table of the above data: Number of members Tally marks Number of families f r e q u e n c y 3 | | | | 4 4 | | | | 4 5 | | | | || 7 6 | | | 3 7 || 2 Total 20 Question:2 A dice was thrown 30 times and the following outcomes were noted: 2, 1, 2, 4, 6, 1, 2, 3, 6, 5, 4, 4, 3, 1, 1, 3, 1, 1, 5, 6, 6, 2, 2, 3, 4, 2, 5, 5, 6, 4. Prepare a frequency table. Solution: Arranging the outcomes in increasing order, we get: 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6 Now, we have: 1 was thrown 6 times 2 was thrown 6 times 3 was thrown 4 times 4 was thrown 5 times 5 was thrown 4 times 6 was thrown 5 times Frequency distribution table of the above data: Number Tally mark frequency 1 | | | | | 6 2 | | | | | 6 3 | | | | 4 4 | | | | 5 5 | | | | 4 6 | | | | 5 Total 30 Marks Tally marks Frequency 0-10 ||| 3 10-20 |||| ||| 8 20-30 |||| |||| |||| 14 30-40 |||| |||| 9 40-50 |||| | 6 Total 40 Question:3 The following data gives the number of children in 40 families: 1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2. Represent it in the form of a frequency distribution. Solution: Arranging the dates in ascending order, we get: 0, 0 ,0 , 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2,2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6 There are: 4 families with no children 7 families with 1 child 12 families with 2 children 5 families with 3 children 6 families with 4 children 3 families with 5 children 3 families with 6 children The frequency distribution table for the above data can be generated as below: Number of children Tally mark Number of families f r e q u e n c y 0 | | | | 4 1 | | | | | | 7 2 | | | | | | | | | | 12 3 | | | | 5 4 | | | | | 6 5 | | | 3 6 | | | 3 Total 40 Question:4 The marks obtained by 40 students of a class in an examination are given below: 8, 47, 22, 31, 17, 13, 38, 26, 3, 34, 29, 11, 22, 7, 15, 24, 38, 31, 21, 35, 42, 24, 45, 23, 21, 27, 29, 49, 25, 48, 21, 15, 18, 27, 19, 45, 14, 34, 37, 34. Prepare a frequency distribution table with equal class intervals, starting from 0-10 w h e r e10 n o t i n c l u d e d . Solution: Arranging the given observations in ascending order, we get: 3, 7, 8, 11, 13, 14, 15, 15, 17, 18, 19, 21, 21, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 29, 29, 31, 31, 34, 34, 34, 35, 37, 38, 38, 42, 45, 45, 47, 48, 49 Thus, the frequency distribution may be represented as shown below: Question:5 The electricity bills i n r u p e e s of 25 houses of a certain locality for a month are given below: 324, 700, 617, 400, 356, 365, 435, 506, 548, 736, 780, 378, 570, 685, 312, 630, 584, 674, 754, 776, 596, 745, 565, 763, 472. Arrange the above data in increasing order and form a frequency table using equal class intervals, starting from 300-400, where 400 is not included. Electricity bills i n R u p e e s Tally marks Frequency 300-400 |||| 5 400-500 ||| 3 500-600 |||| | 6 600-700 |||| 4 700-800 |||| || 7 Total 25 Weekly wages i n R u p e e s Tally marks Frequency 610-630 |||| 4 630-650 |||| 4 650-670 |||| 5 670-690 ||| 3 690-710 |||| || 7 710-730 |||| 5 Total 28 Weekly pocket expenses i n R u p e e s Tally marks Frequency 60-70 |||| | 6 70-80 |||| 5 80-90 |||| || 7 90-100 |||| 5 100-110 ||| 3 110-120 |||| 4 Total 30 Solution: Arranging the given observations in increasing order, we get: 312, 324, 356, 365, 378, 400, 435, 472, 506, 548, 565, 570, 584, 596, 617, 630, 674, 685, 700, 736, 745, 754, 763, 776, 786 Thus, the frequency distribution may be represented as shown below: Question:6 The weekly wages i n r u p e e s of 28 workers of a factory are given below: 668, 610, 642, 658, 668, 620, 719, 720, 700, 690, 710, 642, 672, 654, 692, 706, 718, 702, 704, 678, 615, 640, 680, 716, 705, 615, 636, 656. Construct a frequency table with equal class intervals, taking the first of the class intervals as 610-630, where 630 is not included. Solution: Arranging the given observations in ascending order, we get: 610, 615, 615, 620, 636, 640, 642, 642, 654, 656, 658, 668, 668, 672, 678, 680, 690, 692, 700, 702, 704, 705, 706, 710, 716, 718, 719, 720 Thus, the frequency distribution may be represented as shown below: Question:7 The weekly pocket expenses i n r u p e e s of 30 students of a class are given below: 62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103, 96, 64, 94, 87, 85, 105, 115. Construct a frequency table with class intervals 60-70 w h e r e70 i s n o t i n c l u d e d , 70-80, 80-90, etc. Solution: Arranging the given observations in increasing order, we get: 60, 62, 62, 64, 65, 68, 72, 72, 73, 75, 78, 80, 80, 84, 85, 86, 87, 87, 90, 94, 94, 95, 96, 100, 103, 105, 110, 115, 117, 118 Thus, the frequency distribution may be represented as given below: Question:8 The daily earnings i n r u p e e s of 24 stores in a market was recorded as under: 715, 650, 685, 550, 573, 530, 610, 525, 742, 680, 736, 524, 500, 585, 723, 545, 532, 560, 580, 545, 625, 630, 645, 700. Prepare a frequency table taking equal class sizes. One such class is 500-550, where 550 is not included. Solution: Arranging the given observations in increasing order, we get: 500, 524, 525, 530, 532, 545, 545, 550, 560, 573, 580, 585, 610, 625, 630, 645, 650, 680, 685, 700, 715, 723, 736, 742 Thus, the frequency distribution may be represented as given below: Daily earnings i n R u p e e s Tally marks Frequency 500-550 ||||| || 7 550-600 ||||| 5 600-650 |||| 4 650-700 ||| 3 700-750 ||||| 5 Total 24 Heights i n c m Tally marks Frequency 125-130 |||| 5 130-135 |||| || 7 135-140 |||| | 6 140-145 |||| 4 Total 22 Question:9 The heights i n c m of 22 students were recorded as under: 125, 132, 138, 144, 142, 136, 134, 125, 135, 130, 126, 132, 135, 142, 143, 128, 126, 136, 135, 130, 130, 133. Prepare a frequency distribution table, taking equal class intervals and starting from 125-130, where 130 is not included. Solution: Arranging the given observations in increasing order, we get 125, 125, 126, 126, 128, 130, 130, 130, 132, 132, 133, 134, 135, 135, 135, 136, 136, 138, 142, 142, 143 and 144. Thus, the frequency distribution may be represented as given below: Question:10 The top speeds of 30 different land animals have been organised into a frequency table given below: Maximum speed i n k m/ h 10–20 20– 30 30– 40 40– 50 50– 60 60– 70 Number of animals 3 5 10 8 0 2 Draw a histogram for the given data. Solution: Question:11 The ages i n y e a r s of 360 patients treated in a hospital on a particular day are given below: Age i n y e a r s 10– 20 20– 30 30– 40 40– 50 50– 60 60– 70 Number of patients 90 40 60 20 120 30 Draw a histogram for the given data. Hint. Take 10 small divisions = 10 patients. Solution: Question:12 Draw a histogram for the frequency distribution of following data: Class interval 8–13 13– 18 18– 23 23– 28 28– 33 33– 38 38– 43 Frequency 320 780 160 540 260 100 80 Hint. Take 1 small division = 10. Solution:Read More

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