1
Question
The frequency distribution of the diameters of neem trees, measured 1 metre above the ground, is shown.
Diameter (in cm)
Number of trees
Below 25
0
Below 50
26
Below 75
68
Below 100
203
Below 125
215
Below 150
220
Prepare the frequency distribution . Draw a less-than type and a more-than type cumulative frequency curve on the same graph paper. Also, find the median.
| Diameter (in cm) | Number of trees |
| Below 25 | 0 |
| Below 50 | 26 |
| Below 75 | 68 |
| Below 100 | 203 |
| Below 125 | 215 |
| Below 150 | 220 |
Prepare the frequency distribution . Draw a less-than type and a more-than type cumulative frequency curve on the same graph paper. Also, find the median.
Open in App
Solution
First, we find the class frequencies from the given less-than cumulative frequencies.
Diameter
(in cm) Frequency
(fi ) Upper boundary
(ui ) Less-than cumulative frequency
(Fi ) Lower boundary
(li ) More-than cumulative frequency (Fi' ) - - 25 0 - - 25-50 26 50 26 25 220 50-75 6826 = 42 75 68 50 215 75-100 20368 = 135 100 203 75 203 100-125 215203 = 12 125 215 100 68 125-150 220215 = 5 150 220 125 26 - - - - 150 0
The median can be obtained by drawing a perpendicular AB to the X-axis from the point of intersection of the two curves .
The foot of the perpendicular is the median. Here, it is 82 cm.
| Diameter (in cm) | Frequency (fi ) | Upper boundary (ui ) | Less-than cumulative frequency (Fi ) | Lower boundary (li ) | More-than cumulative frequency (Fi' ) |
| - | - | 25 | 0 | - | - |
| 25-50 | 26 | 50 | 26 | 25 | 220 |
| 50-75 | 6826 = 42 | 75 | 68 | 50 | 215 |
| 75-100 | 20368 = 135 | 100 | 203 | 75 | 203 |
| 100-125 | 215203 = 12 | 125 | 215 | 100 | 68 |
| 125-150 | 220215 = 5 | 150 | 220 | 125 | 26 |
| - | - | - | - | 150 | 0 |
The median can be obtained by drawing a perpendicular AB to the X-axis from the point of intersection of the two curves .
The foot of the perpendicular is the median. Here, it is 82 cm.
Suggest Corrections
0
Similar questions