GATE 2026 IN Q.31: solution and answer

Official answer: 1Source: Official answer key, GATE 2026 IN (IIT Guwahati)

1. Count the observations. There are $n=9$ values. Since $n$ is odd, the median is a single middle value, not the average of two.

2. Sort the data in ascending order: $$-3,-1,0,0,1,1,1,2,2$$ (Check: the list still has nine entries, with one $-3$, one $-1$, two $0$s, three $1$s and two $2$s, the same as the given set.)

3. For odd $n$ the median is at position $\frac{n+1}{2}=\frac{9+1}{2}=5$, so take the 5th value of the sorted list.

4. Read off the 5th value. The first four are $-3,-1,0,0$, and the 5th is $1$. So the median is $1$.

5. Check: four values ($-3,-1,0,0$) sit before the 5th position and four ($1,1,2,2$) sit after it, so the median splits the data in half as it should. $1$ is already an integer, so rounding leaves it unchanged.