Calculate the median for the following data:
Age (in years) | 19 - 25 | 26 - 32 | 33 - 39 | 40 - 46 | 47 - 53 | 54 - 60 |
Frequency | 35 | 96 | 68 | 102 | 35 | 4 |
To find median, Assume
Σfi = N = Sum of frequencies,
h = length of median class,
l = lower boundary of the median class,
f = frequency of median class
and Cf = cumulative frequency
Lets form a table and convert it into exclusive - type by adjusting from both ends of a class.
AGE(years) | FREQUENCY(fi) | Cf |
18.5 - 25.5 | 35 | 35 |
25.5 - 32.5 | 96 | 35 + 96 = 131 |
32.5 - 39.5 | 68 | 131 + 68 = 199 |
39.5 - 46.5 | 102 | 199 + 102 = 301 |
46.5 - 53.5 | 35 | 301 + 35 = 336 |
53.5 - 60.5 | 4 | 336 + 4 = 340 |
TOTAL | 340 |
So, N = 340
⇒ N/2 = 340/2 = 170
The cumulative frequency just greater than (N/2 = ) 170 is 199, so the corresponding median class is 32.5 - 39.5 and accordingly we get Cf = 131(cumulative frequency before the median class).
Now, since median class is 32.5 - 39.5.
∴ l = 32.5, h = 7, f = 68, N/2 = 170 and Cf = 131
Median is given by,
⇒ 
= 32.5 + 4.014
= 36.51
Thus, median is 36.51 years.