Consider the following distribution:
Class interval | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 |
Frequency | 10 | 15 | 12 | 20 | 9 |
The Sum of the lower limits of the median class and the modal class is
We need to find – (1) Median class
(2) Modal class
First we’ll find (1) Median class.
To find median class,
Assume Σfi = N = Sum of frequencies,
fi = frequency of class intervals
and Cf = cumulative frequency
Lets form a table.
CLASS INTERVAL | FREQUENCY(fi) | Cf |
0 - 5 | 10 | 10 |
5 - 10 | 15 | 10 + 15 = 25 |
10 - 15 | 12 | 25 + 12 = 37 |
15 - 20 | 20 | 37 + 20 = 57 |
20 - 25 | 9 | 57 + 9 = 66 |
TOTAL | 66 |
So, N = 66
⇒ N/2 = 66/2 = 33
The cumulative frequency just greater than (N/2 = ) 33 is 37, so the corresponding median class is 10 - 15.
∴ median class is 10 - 15.
To find (2) Modal class,
Here, the maximum class frequency is 20.
The class corresponding to this frequency is the modal class. ⇒ modal class = 15 - 20
Lower limit of median = 10 and lower limit of mode = 15
Sum = 10 + 15 = 25