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प्रश्न
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 |
उत्तर
| Age in years (less than) |
Cumulative Frequency |
| 10 | 0 |
| 20 | 17 |
| 30 | 32 |
| 40 | 37 |
| 50 | 53 |
| 60 | 58 |
| 70 | 65 |
Steps of construction:
- Plot the points (10, 0), (20, 17), (30, 32), (40, 37), (50, 53), (60, 58) and (70, 65) on the graph.
- Join them with free hand to obtain an ogive.
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संबंधित 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.
Draw an ogive to represent the following frequency distribution:
| Class-interval: | 0 - 4 | 5 - 9 | 10 - 14 | 15 - 19 | 20 - 24 |
| Frequency: | 2 | 6 | 10 | 5 | 3 |
The following table gives the height of trees:
| Height | No. of trees |
| Less than 7 Less than 14 Less than 21 Less than 28 Less than 35 Less than 42 Less than 49 Less than 56 |
26 57 92 134 216 287 341 360 |
Draw 'less than' ogive and 'more than' ogive.
The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution:
| Profit (in lakhs in Rs) | Number of shops (frequency) |
| More than or equal to 5 More than or equal to 10 More than or equal to 15 More than or equal to 20 More than or equal to 25 More than or equal to 30 More than or equal to 35 |
30 28 16 14 10 7 3 |
Draw both ogives for the above data and hence obtain the median.
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 |
Draw an ogive for the following :
| Class Interval | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 |
| Frequency | 28 | 23 | 15 | 20 | 14 |
The marks obtained by 100 students of a class in an examination are given below.
| Marks | No. of students |
| 0-5 | 2 |
| 5-10 | 5 |
| 10-15 | 6 |
| 15-20 | 8 |
| 20-25 | 10 |
| 25-30 | 25 |
| 30-35 | 20 |
| 35-40 | 18 |
| 40-45 | 4 |
| 45-50 | 2 |
Draw 'a less than' type cumulative frequency curves (orgive). Hence find median
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 |
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.
