(b) Both assertion (A) and reason (R) are true, but reason (R) is not a correct explanation of assertion (A).
Clearly, reason (R) is true.
The maximum frequency is 23 and the modal class is 12 – 15.
Now, xk = 12, fk = 23, fk-1= 21, fk+1 = 23 and h = 3
∴ Mode = \(\{12+3\times\frac{(23-21)}{(2\times23-21-10)}\}\)
= \((12+3\times\frac{2}{15})\)
= (12 +0.4)
= 12
∴ Assertion (A) is true.
However, reason (R) is not a correct explanation of assertion (A).