UPSC NDA I 2022 Mathematics Solved Paper

Concept:The sum of deviations (signed differences) of data points from the median is zero when the distribution is symmetric. For an arithmetic progression, the median equals the mean.Explanation:The given AP is $4, 7, 10, \ldots, 151, 154$ with $n = 51$ terms.Median of an AP with odd number of terms is the middle term, which equals $\frac{\text{first} + \text{last}}{2} = \frac{4 + 154}{2} = 79$.Deviations from median are: $(4-79), (7-79), \ldots, (151-79), (154-79)$.These form a symmetric set: $(-75, -72, \ldots, 72, 75)$.Each positive term cancels the corresponding negative term, so the total sum is $0$.Answer:$0$ (Option B).