Consider the frequency distribution of the heights of 60 students of a class:
Height (in cm) | No of Students | Cumulative Frequency |
150 - 155 | 16 | 16 |
155 - 160 | 12 | 28 |
160 - 165 | 9 | 37 |
165 - 170 | 7 | 44 |
170 - 175 | 10 | 54 |
175 - 180 | 6 | 60 |
The Sum of the lower limit of the modal class and the upper limit of the median class is
To find median class,
Assume Σfi = N = Sum of frequencies,
fi = frequency
and Cf = cumulative frequency
HEIGHT (in cm) | NUMBER OF STUDENTS | CUMULATIVE FREQUENCY (Cf) |
150 - 155 | 16 | 16 |
155 - 160 | 12 | 28 |
160 - 165 | 9 | 37 |
165 - 170 | 7 | 44 |
170 - 175 | 10 | 54 |
175 - 180 | 6 | 60 |
TOTAL | 60 |
So, N = 60
⇒ N/2 = 60/2 = 30
The cumulative frequency just greater than (N/2 = ) 30 is 37, so the corresponding median class is 160 - 165.
∴ upper limit of median class = 165
For modal class,
Here, the maximum class frequency is 16.
The class corresponding to this frequency is the modal class. ⇒ modal class = 150 - 155
∴ lower limit of the modal class = 150
Hence, Sum of lower limit of the modal class and upper limit of the median class = 165 + 150 = 315