The following table gives the heights of plants (in cm) in a garden.
Height(in cm)
Less than 8
Less than 16
Less than 24
Less than 32
Less than 40
Less than 48
Less than 56
No: of plants
22
43
83
118
176
256
300
Draw a more than ogive for the above data and hence determine the median from it
Dear student,
Plotting the more than ogive by taking cumulative frequency on y-axis and more than height on x-axis,
To find the median,
Find the (N/2)thitem, where N is the total number of trees in the given data, and mark it on the y-axis.In this case the (N/2)th item (trees) is 300/2 = 150. Draw a perpendicular from 150 to the right to cut the Ogive curve at point A. From point A where the Ogive curve is cut, draw a perpendicular on the x-axis. The point at which it touches the x-axis (which will be between 32 and 40) will be the median value of the series. SO, 32-40 will be the median class.
Regards
| HEIGHT (LESS THAN) |
CLASS INTERVAL | FREQUENCY | HEIGHT (MORE THAN) |
CUMULATIVE FREQUENCY |
| 8 |
0-8 | 22 | 0 | 300 |
| 16 | 8-16 | 21(=43-22) | 8 | 278(=300-22) |
| 24 | 16-24 | 40(=83-43) | 16 | 257(=278-21) |
| 32 | 24-32 | 35(=118-83) | 24 | 217(=257-40) |
| 40 | 32-40 | 58(=176-118) | 32 | 182(=217-35) |
| 48 | 40-48 | 80(=256-176) | 40 | 124(=182-58) |
| 56 | 48-56 | 44(=300-256) | 48 | 44(=124-80) |
Plotting the more than ogive by taking cumulative frequency on y-axis and more than height on x-axis,
To find the median,
Find the (N/2)thitem, where N is the total number of trees in the given data, and mark it on the y-axis.In this case the (N/2)th item (trees) is 300/2 = 150. Draw a perpendicular from 150 to the right to cut the Ogive curve at point A. From point A where the Ogive curve is cut, draw a perpendicular on the x-axis. The point at which it touches the x-axis (which will be between 32 and 40) will be the median value of the series. SO, 32-40 will be the median class.
Regards