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प्रश्न
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.
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उत्तर
Draw the cumulative frequency table.
| Marks | Number of Students (Frequency) | Cumulative Frequency |
| 0-10 | 3 | 3 |
| 10-20 | 7 | 10 |
| 20-30 | 12 | 22 |
| 30-40 | 17 | 39 |
| 40-50 | 23 | 62 |
| 50-60 | 14 | 76 |
| 60-70 | 9 | 85 |
| 70-80 | 6 | 91 |
| 80-90 | 5 | 96 |
| 90-100 | 4 | 100 |
Scale: On x-axis, 1 unit = 10 marks, On y-axis, 1 unit = 10 students
1) Median = `(N/2)^"th" term = (100/2)^"th" term = 50^"th term"`
Draw a horizontal line through mark 50 on the y-axis. The, draw a vertical line from the point it cuts on the graph. The point this line touches the x-axis is the median. Thus, median = 45
2) Lower quartile = `(N/4)^"th" term = (100/4)^"th" term = 25^"th term"`
Draw a horizontal line through mark 25 on the y-axis. The, draw a vertical line from the point it cuts on the graph. The point this line touches the x-axis is the lower quartile
Thus, lower quartile = 31
3) Draw a vertical line through mark 85 on the x-axis. Then, draw a horizontal line from the point it cuts on the graph.
The point where this line touches the y-axis is the number of students who obtained less than 85% marks =93
Thus, number of students who obtained more than 85% marks =100 – 93 = 7
4) Draw a vertical line through mark 35 on the x-axis. The, draw a horizontal line from the point it cuts on the graph.
The point where this line touches the y-axis is the number of students who obtained less than 35% marks = 21
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संबंधित 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.
Draw a cumulative frequency curve (ogive) for the following distributions:
| Class Interval | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |
| Frequency | 10 | 15 | 17 | 12 | 10 | 8 |
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 distributions:
| Age in years (less than) | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
| Cumulative frequency | 0 | 17 | 32 | 37 | 53 | 58 | 65 |
Find the correct answer from the alternatives given.
Cumulative frequencies in a grouped frequency table are useful to find ______.
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 |
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.
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 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.
