Advertisements
Advertisements
Question
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 |
Advertisements
Solution
The above distribution is discontinuous converting into continuous distribution, we get:
Adjustment factor = `("Lower limit of one class" - "Upper limit of previous class") / 2`
= `(20 - 19)/2`
= `1/2`
= 0.5
Subtract the adjustment factor (0.5) from all the lower limits and add the adjustment factor (0.5) to all the upper limits.
| Class Interval (Inclusive) | Class Interval (Exclusive) | Frequency | Cumulative Frequency |
| 10 – 19 | 9.5 – 19.5 | 23 | 23 |
| 20 – 29 | 19.5 – 29.5 | 16 | 39 |
| 30 – 39 | 29.5 – 39.5 | 15 | 54 |
| 40 – 49 | 39.5 – 49.5 | 20 | 74 |
| 50 – 59 | 49.5 – 59.5 | 12 | 86 |
| Total | 86 |
Steps of construction of ogive:
- Since, the scale on x-axis starts at 9.5, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 9.5.
- Take 2 cm = 10 units along the x-axis.
- Take 1 cm = 10 units along the y-axis.
- Ogive always starts from a point on the x-axis, representing the lower limit of the first class. Mark point (9.5, 0).
- Take upper-class limits along the x-axis and corresponding cumulative frequencies along the y-axis, and mark the points (19.5, 23), (29.5, 39), (39.5, 54), (49.5, 74) and (59.5, 86).
- Join the points marked by a free-hand curve.
The required ogive is shown in the below figure:
RELATED QUESTIONS
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 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.
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 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 |
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 :
| 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 |
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.
