In the following data, find the values of p and q. Also, find the median class and modal class.
Class | Frequency (f) | cummulative frequency (cf) |
100 - 200 | 11 | 11 |
200 - 300 | 12 | P |
300 - 400 | 10 | 33 |
400 - 500 | Q | 46 |
500 - 600 | 20 | 66 |
600 - 700 | 14 | 80 |
To find p and q, solve by finding cumulative frequency,
CLASS | FREQUENCY (f) | CUMULATIVE FREQUENCY (Cf) |
100 - 200 | 11 | 11 |
200 - 300 | 12 | p = 11 + 12 = 23 |
300 - 400 | 10 | 33 |
400 - 500 | q | 46 = 33 + q ⇒ q = 13 |
500 - 600 | 20 | 66 |
600 - 700 | 14 | 80 |
⇒ p = 11 + 12 = 23
And 46 = 33 + q ⇒ q = 46 – 33 = 13
∴ p = 23 and q = 13
Lets form the table again,
CLASS | FREQUENCY (fi) | CUMULATIVE FREQUENCY (Cf) |
100 - 200 | 11 | 11 |
200 - 300 | 12 | 23 |
300 - 400 | 10 | 33 |
400 - 500 | 13 | 46 |
500 - 600 | 20 | 66 |
600 - 700 | 14 | 80 |
TOTAL | 80 |
For modal class,
Here, the maximum class frequency is 20.
The class corresponding to this frequency is the modal class. ⇒ modal class = 500 - 600
To find median class,
Assume Σfi = N = Sum of frequencies,
fi = frequency
and Cf = cumulative frequency
So, N = 80
⇒ N/2 = 80/2 = 40
The cumulative frequency just greater than (N/2 = ) 40 is 46, so the corresponding median class is 400 - 500.
∴ modal class = 500 - 600 and median class = 400 - 500