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प्रश्न
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.
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उत्तर
The cumulative frequency table of the given distribution table is as follows:
| Weight in Kg | Number of workers | Cumulative frequency |
| 50-60 | 4 | 4 |
| 60-70 | 7 | 11 |
| 70-80 | 11 | 22 |
| 80-90 | 14 | 36 |
| 90-100 | 6 | 42 |
| 100-110 | 5 | 47 |
| 110-120 | 3 | 50 |
The ogive is as follows:
Number of worker = 50
1) Upper quartile (Q3) = `((3 xx 50)/4)^"th"` term = `(37.5)^th` term = 92
Lower quartile (`Q_1`) = `(50/4)^"th"` term = `(12.5)^"th"` term = 71.1
2) Through mark of 95 on the x-axis, draw a vertical line which meets the graph at point C.
Then through point C, draw a horizontal line which meets the y-axis at the mark of 39
Thus, number of workers weighing 95 kg and above = 50 - 39 = 11
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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 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 |
Construct a frequency distribution table for the following distributions:
| Marks (less than) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| Cumulative frequency | 0 | 7 | 28 | 54 | 71 | 84 | 105 | 147 | 180 | 196 | 200 |
Construct a frequency distribution table for the following distributions:
| Marks (more than) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| Cumulative frequency | 100 | 87 | 65 | 55 | 42 | 36 | 31 | 21 | 18 | 7 | 0 |
Draw an ogive for the following :
| Class Interval | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 | 350-400 |
| Frequency | 10 | 13 | 17 | 12 | 10 | 8 |
Draw an ogive for the following :
| Marks obtained | More than 10 | More than 20 | More than 30 | More than 40 | More than 50 |
| No. of students | 8 | 25 | 38 | 50 | 67 |
Find the width of class 35 - 45.
The following is the frequency distribution with unknown frequencies :
| Class | 60-70 | 70-80 | 80-90 | 90-100 | Total |
| frequency | `"a"/2` | `(3"a")/2` | 2a | a | 50 |
Find the value of a, hence find the frequencies. Draw a histogram and frequency polygon on the same coordinate system.
Cumulative frequency curve is also called ______.
