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प्रश्न
Using a graph paper, drawn an Ogive for the following distribution which shows a record of the weight in kilograms of 200 students.
| Weight | Frequency |
| 40 - 45 | 5 |
| 45 - 50 | 17 |
| 50 - 55 | 22 |
| 55 - 60 | 45 |
| 60 - 65 | 51 |
| 65 - 70 | 31 |
| 70 - 75 | 20 |
| 75 - 80 | 9 |
Use your ogive to estimate the following:
(i) The percentage of students weighing 55kg or more.
(ii) The weight above which the heaviest 30% of the students fall.
(iii) The number of students who are:
(1) under-weight and
(2) over-weight, if 55·70 kg is considered as standard weight.
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उत्तर
| Weight | Frequency | c.f. |
| 40 - 45 | 5 | 5 |
| 45 - 50 | 17 | 22 |
| 50 - 55 | 22 | 44 |
| 55 - 60 | 45 | 89 |
| 60 - 65 | 51 | 140 |
| 65 - 70 | 31 | 171 |
| 70 - 75 | 20 | 191 |
| 75 - 80 | 9 | 200 |
(i) Number of student weighing 55 kg or more
= 200 - 44
= 156
∴ Percentage = `(156 xx 100)/(200)`
= 78%.
(ii) 30% of 200 = 60
∴ Heaviest w.t. (least)
= w.t. of 200 - 60
= 140th student
= 65 kg or more.
(iii) From ogive c.f. against 55.70 kg
= 45
∴ (1) number of under w.t. students
= 44
(2) number of over w.t. students
= 200 - 44
= 156.
संबंधित प्रश्न
The daily wages of 80 workers in a project are given below.
| Wages (in Rs.) |
400-450 | 450-500 | 500-550 | 550-600 | 600-650 | 650-700 | 700-750 |
| No. of workers |
2 | 6 | 12 | 18 | 24 | 13 | 5 |
Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:
- the median wage of the workers.
- the lower quartile wage of workers.
- the numbers of workers who earn more than Rs. 625 daily.
The weight of 50 workers is given below:
| Weight in Kg | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 | 100-110 | 110-120 |
| No. of Workers | 4 | 7 | 11 | 14 | 6 | 5 | 3 |
Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:
1) The upper and lower quartiles.
2) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight.
The marks obtained by 100 students in a Mathematics test are given below:
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No. of students |
3 | 7 | 12 | 17 | 23 | 14 | 9 | 6 | 5 | 4 |
Draw an ogive for the given distribution on a graph sheet.
Use a scale of 2 cm = 10 units on both axes.
Use the ogive to estimate the:
1) Median.
2) Lower quartile.
3) A number of students who obtained more than 85% marks in the test.
4) A number of students who did not pass in the test if the pass percentage was 35.
Draw an ogive by less than method for the following data:
| No. of rooms: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| No. of houses: | 4 | 9 | 22 | 28 | 24 | 12 | 8 | 6 | 5 | 2 |
Draw a cumulative frequency curve (ogive) for the following distributions:
| Class Interval | 10 – 19 | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 |
| Frequency | 23 | 16 | 15 | 20 | 12 |
Draw an ogive for the following :
| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 8 | 12 | 10 | 14 | 6 |
Draw an ogive for the following :
| Class Interval | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 |
| Frequency | 28 | 23 | 15 | 20 | 14 |
Draw an ogive for the following :
| Age in years | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 |
| No. of people | 0 | 17 | 42 | 67 | 100 |
Prepare the cumulative frequency (less than types) table from the following distribution table :
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 2 | 3 | 7 | 8 | 5 |
The frequency distribution of scores obtained by 230 candidates in a medical entrance test is as ahead:
| Cost of living Index | Number of Months |
| 400 - 450 | 20 |
| 450 - 500 | 35 |
| 500 - 550 | 40 |
| 550 - 600 | 32 |
| 600 - 650 | 24 |
| 650 - 700 | 27 |
| 700 - 750 | 18 |
| 750 - 800 | 34 |
| Total | 230 |
Draw a cummulative polygon (ogive) to represent the above data.
