Marks 0 1 2 3 4 5 Frequency 7 4 18 12 8 11 The table gives the distribution of marks obtained by a number of…

Analyze the question: We need the first quartile (Q1) of a discrete frequency distribution.

Concept: Q1 is the value below which 25% of the data lies. Find the cumulative frequency (CF), then locate the position of Q1, which is ¼ of the total frequency (N).

Solution:

| Marks | Frequency | Cumulative Frequency | |---|---|---| | 0 | 7 | 7 | | 1 | 4 | 11 | | 2 | 18 | 29 | | 3 | 12 | 41 | | 4 | 8 | 49 | | 5 | 11 | 60 |

Total N = 60.

Position of Q1 = ¼ × 60 = 15th value (or, using (N+1)/4, the 15.25th value).

Check the cumulative frequencies:

• Marks 0 and 1 cover positions 1 to 11.
• Marks of 2 cover positions 12 to 29.

The 15th (and 16th) value falls within the group with 2 marks, so Q1 = 2.

Answer: Q1 = 2.0, which is option C.

Tip: For discrete data, find N/4 and look at the cumulative frequency column. The first mark whose cumulative frequency reaches or exceeds that position is your quartile. Do the same with N/2 for the median and 3N/4 for Q3.