Q.In a continuous series, the class containing P50 must be the same class as:

P50, Q2 and the median all locate the identical 50% position in a series, so they always fall in the same class. …

Checking each option:

• (a) The modal class is the class with the HIGHEST frequency — this has no necessary connection to the 50% cumulative position, and can be an entirely different class from the one containing P50.
• (b) The class containing Q2 — since $P_{50}=Q_2=\text{Median}$ exactly (Section 5), both are located using the identical position $k=N/2$, so they must fall in the SAME class, always. …

Assuming the mean, median and mode must all fall in the same class — this is only exactly true for a perfectly symmetrical distribution (Measures of Central Tendency, Section 9); P50 and Q2 are guaranteed to coincide for a much more ba …