Find the median of the following data by making a 'less than ogive'.
Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
Number of students | 5 | 3 | 4 | 3 | 3 | 4 | 7 | 9 | 7 | 8 |
The frequency distribution table for ‘less than’ type is:
MARKS | CUMULATIVE FREQUENCY (Cf) |
Less than 10 | 5 |
Less than 20 | 5 + 3 = 8 |
Less than 30 | 8 + 4 = 12 |
Less than 40 | 12 + 3 = 15 |
Less than 50 | 15 + 3 = 18 |
Less than 60 | 18 + 4 = 22 |
Less than 70 | 22 + 7 = 29 |
Less than 80 | 29 + 9 = 38 |
Less than 90 | 38 + 7 = 45 |
Less than 100 | 45 + 8 = 53 |
Lets plot a graph of ‘less than ogive’, taking upper limits of the class intervals on x - axis and cumulative frequencies on y - axis.
As we have N = 53 by the frequency table.
N/2 = 53/2 = 26.5
Mark 26.5 on y - axis and the corresponding point on x - axis would be the median.
The corresponding point on x - axis is 66.4.
Hence, median is 66.4