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प्रश्न
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.
उत्तर
Firstly, we prepare the cumulative frequency table for less than type.
Profit (In lakh in Rs.) |
No. of shops (frequency) |
Profit (less than) |
Cumulative frequency |
Suitable points |
| 5-10 | 2 | 10 | 2 | (10, 2) |
| 10-15 | 12 | 15 | 14 | (15, 14) |
| 15-20 | 2 | 20 | 16 | (20, 16) |
| 20-25 | 4 | 25 | 20 | (25, 20) |
| 25-30 | 3 | 30 | 23 | (30, 23) |
| 30-35 | 4 | 35 | 27 | (35, 27) |
| 35-40 | 3 | 40 | 30 | (40, 30) |
Again, prepare the cumulative frequency table for more than type.
Profit (In lakh in Rs.) |
No. of shops (frequency) |
Profit (more than) |
Cumulative |
Suitable |
| 5-10 | 2 | 5 | 30 | (5, 30) |
| 10-15 | 12 | 10 | 28 | (10, 28) |
| 15-20 | 2 | 15 | 16 | (15, 16) |
| 20-25 | 4 | 20 | 14 | (20, 14) |
| 25-30 | 3 | 25 | 10 | (25, 10) |
| 30-35 | 4 | 30 | 7 | (30, 7) |
| 35-40 | 3 | 35 | 3 | (35, 3) |
Now, “more than ogive” and “less than ogive” can be drawn as follows:
The x-coordinate of the point of intersection of the “more-than ogive” and “less-than ogive” gives the median of the given distribution..
So, the corresponding median is Rs 17.5 lakh.
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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.
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.
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 |
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 | 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 | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 |
| No. of students | 8 | 22 | 48 | 60 | 75 |
Draw an ogive for the following :
| 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 |
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
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.
Cumulative frequency curve is also called ______.
