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1. Given below are the marks (out of 100) in English obtained by 40 students of a class in an annual examination.
90, 36, 55, 78, 85, 96, 56, 77, 63, 53, 75, 56, 91, 86, 82, 29, 46, 40, 88, 76, 77, 79, 83, 85, 69, 64, 45, 67, 62, 60, 36, 39, 48, 49, 50, 73, 86, 88, 89, 92
Arrange the above data in ascending order and find
(i) the lowest marks obtained,
(ii) the highest marks obtained,
(iii) the range of the given data.
Solution:
Given that,
The marks of 40 students of a class in English are 90, 36, 55, 78, 85, 96, 56, 77, 63, 53, 75, 56, 91, 86, 82, 29, 46, 40, 88, 76, 77, 79, 83, 85, 69, 64, 45, 67, 62, 60, 36, 39, 48, 49, 50, 73, 86, 88, 89, 92
The ascending order of the students marks are 29, 36, 36, 39, 40, 45, 46, 48, 49, 50, 53, 55, 56, 56, 60, 62, 63, 64, 67, 69, 73, 75, 76, 77, 77, 78, 79, 82, 83, 85, 85, 86, 86, 88, 88, 89, 90, 91, 92, 96
From the above data analysis, we can say that
The lowest marks obtained is 29.
The highest marks obtained is 96.
The range of the data is 96 – 29 = 67.
2. The weight (in Kgs) of 20 students who are playing sports daily is 56, 68, 43, 55, 58, 59, 52, 50, 46, 49, 50, 44, 45, 68, 67, 64, 60, 62, 55, 49
Arrange the above data in ascending order and find
(i) the lowest weight of the student,
(ii) the highest weight of the student,
(iii) the range of the given data.
Solution:
Given that,
The weight os 20 students is 56, 68, 43, 55, 58, 59, 52, 50, 46, 49, 50, 44, 45, 68, 67, 64, 60, 62, 55, 49
The ascending order of the students weight is 43, 44, 45, 46, 49, 49, 50, 50, 52, 55, 55, 56, 58, 59, 60, 62, 64, 67, 68, 68
From the above data analysis, we can say that
The lowest weight of the student is 43 Kgs
The highest weight of the students is 68 Kgs
Range is 68 – 43 = 25.
3. A dice was thrown 25 times and the following outcomes were noted:
1, 5, 6, 2, 3, 4, 2, 5, 6, 1, 5, 2, 3, 4, 5, 6, 5, 2, 1, 4, 3, 6, 2, 5, 1
Prepare a frequency distribution of data.
Solution:
Given that,
The noted outcomes of a dice are 1, 5, 6, 2, 3, 4, 2, 5, 6, 1, 5, 2, 3, 4, 5, 6, 5, 2, 1, 4, 3, 6, 2, 5, 1
Arranging the data in ascending order, we get the observations as 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6
The lowest value is 1, the highest value is 6, the range is 6 – 1 = 5
From the data, we find that
1 was observed 4 times,
2 was observed 5 times,
3 was observed 3 times,
4 was observed 3 times,
5 was observed 6 times,
6 was observed 4 times,
We may represent the above data in a tabular form, showing the frequency of each observation. The number of times data occurs in a data set is known as the frequency of data
This tabular form of representation is called a frequency distribution.
| Dice Outcome | Frequency |
|---|---|
| 1 | 4 |
| 2 | 5 |
| 3 | 3 |
| 4 | 3 |
| 5 | 6 |
| 6 | 4 |
| Total | 25 |
4. The daily earnings (in dollars) of 30 stores in a market was recorded as under:
720, 450, 420, 560, 650, 750, 410, 420, 720, 600, 590, 595, 585, 860, 460, 489, 700, 710, 890, 850, 840, 845, 888, 830, 720, 420, 420, 560, 550, 555
Prepare a frequency distribution of data.
Solution:
Given that,
The daily earnings of 30 stores in a market is 720, 450, 420, 560, 650, 750, 410, 420, 720, 600, 590, 595, 585, 860, 460, 489, 700, 710, 890, 850, 840, 845, 888, 830, 720, 420, 420, 560, 550, 555
The ascending order of the data is 410, 420, 420, 420, 420, 450, 460, 489, 550, 555, 560, 560, 585, 590, 595, 600, 650, 700, 710, 720, 720, 720, 750, 830, 840, 845, 850, 860, 888, 890
The lowest value is 410 dollars, the highest value is 890 dollars and the range is 890 – 410 = 480.
From the data, we can design a frequency distribution table.
| Daily Earnings of the Store | Frequency |
|---|---|
| 410 | 1 |
| 420 | 4 |
| 450 | 1 |
| 460 | 1 |
| 489 | 1 |
| 550 | 1 |
| 555 | 1 |
| 560 | 2 |
| 585 | 1 |
| 595 | 1 |
| 600 | 1 |
| 650 | 1 |
| 700 | 1 |
| 710 | 1 |
| 720 | 3 |
| 750 | 1 |
| 830 | 1 |
| 840 | 1 |
| 845 | 1 |
| 850 | 1 |
| 860 | 1 |
| 888 | 1 |
| 890 | 1 |
| Total | 30 |
5. The heights (in cm) of 23 students were recorded as under:
129, 126, 130, 131, 145, 140, 139, 129, 128, 125, 141, 140, 130, 131, 126, 127, 126, 128, 125, 131, 133, 135, 136
Prepare a frequency distribution of data.
Solution:
Given that,
The heights of 23 students in a class are 129, 126, 130, 131, 145, 140, 139, 129, 128, 125, 141, 140, 130, 131, 126, 127, 126, 128, 125, 131, 133, 135, 136
The ascending order of the data is
125, 125, 126, 126, 126, 127, 128, 128, 129, 129, 130, 130, 131, 131, 131, 133, 135, 136, 139, 140, 140, 141, 145
The lowest height of a student is 125 cm, the top height of a student is 145 cm, range is 145 – 125 = 20
From the data, we can design a frequency distribution table.
| Height | Frequency |
|---|---|
| 125 | 2 |
| 126 | 3 |
| 127 | 1 |
| 128 | 2 |
| 129 | 2 |
| 130 | 2 |
| 131 | 2 |
| 133 | 1 |
| 135 | 1 |
| 136 | 1 |
| 139 | 1 |
| 140 | 2 |
| 141 | 1 |
| 145 | 1 |
| Total | 23 |
6. The marks obtained by 50 students of a class in a quiz are given below:
15, 20, 25, 12, 18, 45, 40, 30, 20, 10, 22, 33, 44, 46, 34, 43, 32, 23, 22, 25, 16, 17, 18, 12, 21, 29, 28, 34, 33, 30, 32, 41, 49, 48, 44, 46, 41, 47, 14, 40, 12, 11, 18, 30, 31, 35, 37, 38, 39, 45
Prepare a frequency distribution table for the grouped data.
Solution:
Given that,
The marks scored by 50 students are 15, 20, 25, 12, 18, 45, 40, 30, 20, 10, 22, 33, 44, 46, 34, 43, 32, 23, 22, 25, 16, 17, 18, 12, 21, 29, 28, 34, 33, 30, 32, 41, 49, 48, 44, 46, 41, 47, 14, 40, 12, 11, 18, 30, 31, 35, 37, 38, 39, 45
The ascending order of the data is 10, 11, 12, 12, 12, 14, 15, 16, 17, 18, 18, 18, 20, 20, 21, 22, 22, 23, 25, 25, 28, 29, 30, 30, 30, 31, 32, 32, 33, 33, 34, 34, 35, 37, 38, 39, 40, 40, 41, 41, 43, 44, 44, 45, 45, 46, 46, 47, 48, 49
From the data, we can say that the least marks scored are 10, the highest marks scored is 49.
Range is 49 – 10 = 39
The intervals should separate the scale into equal parts. We could choose intervals of 4. We then begin the scale with 10 and end with 49.
Frequency Distribution Table for Grouped Data is
| Marks Scored | Frequency |
|---|---|
| 10 – 13 | 5 |
| 14 – 17 | 4 |
| 18 – 21 | 6 |
| 22 – 25 | 5 |
| 26 – 29 | 2 |
| 30 – 33 | 8 |
| 34 – 37 | 4 |
| 38 – 41 | 6 |
| 42 – 45 | 5 |
| 46 – 49 | 5 |
| Total | 50 |
7. The weekly wages (in dollars) of 26 workers of a factory are given below:
650, 620, 750, 800, 610, 600, 640, 650, 660, 670, 680, 710, 720, 730, 710, 750, 650, 660, 630, 500, 700, 750, 760, 780, 777, 720
Construct a frequency distribution table for the grouped data.
Solution:
Given that,
The weekly wages of 26 workers of a factory are 650, 620, 750, 800, 610, 600, 640, 650, 660, 670, 680, 710, 720, 730, 710, 750, 650, 660, 630, 500, 700, 750, 760, 780, 777, 720
The ascending order of the data is
500, 600, 610, 620, 630, 640, 650, 650, 650, 660, 660, 670, 680, 700, 710, 710, 720, 720, 730, 750, 750, 750, 760, 777, 780, 800
The lowest value is 500, the highest value is 800, and the range is 800 – 500 = 300
The intervals should separate the scale into equal parts. We could choose intervals of 50. We then begin the scale with 500 and end with 800.
Frequency Distribution Table for Grouped Data is
| Weekly Wages | Frequency |
|---|---|
| 500 – 550 | 1 |
| 551 – 600 | 1 |
| 601 – 650 | 7 |
| 651 – 700 | 5 |
| 701 – 750 | 8 |
| 751 – 800 | 4 |
| Total | 26 |
8. The weekly pocket expenses (in dollars) of 30 students of a class are given below:
80, 50, 60, 65, 55, 52, 51, 60, 64, 100, 90, 89, 98, 56, 65, 57, 75, 76, 67, 53, 70, 74, 75, 86, 93, 98, 82, 83, 94, 96
Prepare a frequency distribution table for the grouped data.
Solution:
Given that,
The weekly pocket expenses of 30 students are 80, 50, 60, 65, 55, 52, 51, 60, 64, 104, 90, 89, 98, 56, 65, 57, 75, 76, 67, 53, 70, 74, 75, 86, 93, 98, 82, 83, 94, 96
The ascending order of the data is 50, 51, 52, 53, 55, 56, 57, 60, 60, 64, 65, 65, 67, 70, 74, 75, 75, 76, 80, 82, 83, 86, 89, 90, 93, 94, 96, 98, 98, 104
The lowest value is 50, the highest value is 104, the range is 104 – 50 = 54
The intervals should separate the scale into equal parts. We could choose intervals of 5. We then begin the scale with 50 and end with 104.
Frequency Distribution Table for Grouped Data is
| Pocket Expenses | Frequency |
|---|---|
| 50 – 54 | 4 |
| 55 – 59 | 3 |
| 60 – 64 | 3 |
| 65 – 69 | 3 |
| 70 – 74 | 2 |
| 75 – 79 | 3 |
| 80 – 84 | 3 |
| 85 – 89 | 2 |
| 90 – 94 | 3 |
| 95 – 99 | 3 |
| 100 – 104 | 1 |
| Total | 30 |
9. The number of members in 20 families are given below:
5, 8, 2, 4, 3, 6, 7, 9, 10, 2, 3, 4, 5, 5, 6, 7, 5, 8, 2, 4
Prepare a frequency distribution of data.
Solution:
Given that,
The number of members in 20 families are 5, 8, 2, 4, 3, 6, 7, 9, 10, 2, 3, 4, 5, 5, 6, 7, 5, 8, 2, 4
The ascending order of the data is 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10
The lowest number is 2, the highest number is 10.
Range is 10 – 2 = 8
We may represent the above data in a tabular form, showing the frequency of each observation. The number of times data occurs in a data set is known as the frequency of data. This tabular form of representation is called a frequency distribution.
| Number of Members | Frequency |
|---|---|
| 2 | 3 |
| 3 | 2 |
| 4 | 3 |
| 5 | 4 |
| 6 | 2 |
| 7 | 2 |
| 8 | 2 |
| 9 | 1 |
| 10 | 1 |
| Total | 20 |
10. The numbers of newspapers sold at a local shop over the 30 days are:
15, 5, 8, 50, 6, 51, 16, 61, 20, 23, 32, 75, 57, 89, 56, 65, 22, 23, 25, 26, 58, 91, 56, 45, 65, 75, 89, 92, 65, 52
State the frequency.
Solution:
Given that,
The numbers of newspapers sold at a local shop are 15, 5, 8, 50, 6, 51, 16, 61, 20, 23, 32, 75, 57, 89, 56, 65, 22, 23, 25, 26, 58, 91, 56, 45, 65, 75, 89, 92, 65, 52
The ascending order of the data is 5, 6, 8, 15, 16, 20, 22, 23, 23, 25, 26, 32, 45, 50, 51, 52, 56, 56, 57, 58, 61, 65, 65, 65, 75, 75, 89, 89, 91, 92
The lowest value is 5, highest value is 92, range is 92 – 5 = 87.
The intervals should separate the scale into equal parts. We could choose intervals of 8. We then begin the scale with 5 and end with 92.
Frequency Distribution Table for Grouped Data is
| Number of Newspapers Sold | Frequency |
|---|---|
| 5 – 12 | 3 |
| 13 – 20 | 3 |
| 21 – 28 | 5 |
| 29 – 36 | 1 |
| 37 – 44 | 0 |
| 45 – 52 | 4 |
| 53 – 60 | 4 |
| 61 – 68 | 4 |
| 69 – 76 | 2 |
| 77 – 84 | 0 |
| 85 – 92 | 3 |
| Total | 30 |
11. The electricity bills (in dollars) of 25 houses of a certain locality for a month are given below:
800, 750, 300, 250, 261, 320, 650, 590, 450, 270, 850, 450, 541, 200, 220, 260, 590, 240, 350, 461, 420, 700, 605, 630, 400
Prepare a frequency distribution table for the grouped data.
Solution:
Given that,
The electricity bills of 25 houses for a month are 800, 750, 300, 250, 261, 320, 650, 590, 450, 270, 850, 450, 541, 200, 220, 260, 590, 240, 350, 461, 420, 700, 605, 630, 400
The ascending order of the data is 200, 220, 240, 250, 260, 261, 270, 300, 320, 350, 400, 420, 450, 450, 461, 541, 590, 590, 605, 630, 650, 700, 750, 800, 850
The lowest value is 200, the highest value is 850, the range is 850 – 200 = 650
The intervals should separate the scale into equal parts. We could choose intervals of 50. We then begin the scale with 200 and end with 650.
Frequency Distribution Table for Grouped Data is
| Electricity Bills | Frequency |
|---|---|
| 200 – 249 | 3 |
| 250 – 299 | 4 |
| 300 – 349 | 2 |
| 350 – 399 | 1 |
| 400 – 449 | 2 |
| 450 – 499 | 3 |
| 500 – 549 | 1 |
| 550 – 599 | 2 |
| 600 – 649 | 2 |
| 650 – 699 | 1 |
| 700 – 749 | 1 |
| 750 – 799 | 1 |
| 800 – 850 | 2 |
| Total | 25 |
12. The weekly pocket expenses (in dollars) of 30 students of a class are given below:
50, 150, 20, 30, 60, 65, 55, 36, 35, 95, 85, 65, 45, 75, 37, 78, 54, 64, 39, 40, 46, 52, 102, 156, 130, 120, 118, 115, 126, 85
Prepare a frequency distribution table for the grouped data.
Solution:
Given that,
The weekly expenses of 30 students are 50, 150, 20, 30, 60, 65, 55, 36, 35, 95, 85, 65, 45, 75, 37, 78, 54, 64, 39, 40, 46, 52, 102, 154, 130, 120, 118, 115, 126, 85
The ascending order of the data is 20, 30, 35, 36, 37, 39, 40, 45, 46, 50, 52, 54, 55, 60, 64, 65, 65, 75, 78, 85, 85, 95, 102, 115, 118, 120, 126, 130, 150, 154
The lowest value is 20, the highest value is 154, the range is 154 – 20 = 134
The intervals should separate the scale into equal parts. We could choose intervals of 15. We then begin the scale with 20 and end with 154.
Frequency Distribution Table for Grouped Data is
| Students Weekly Expenses | Frequency |
|---|---|
| 20 – 34 | 2 |
| 35 – 49 | 7 |
| 50 – 64 | 6 |
| 65 – 79 | 4 |
| 80 – 94 | 2 |
| 95 – 109 | 2 |
| 110 – 124 | 3 |
| 125 – 139 | 2 |
| 140 – 154 | 2 |
| Total | 30 |