NIMCET 2026 — Mathematics PYQ

For the mean, mode, and median to be equal, the data distribution must be perfectly symmetric.

Step 1: Calculate the mean

The sum of the 9 observations is:

$$10+4+11+6+17+15+9+8+x=80+x$$

$$\text{Mean}=\frac{80+x}{9}$$

Step 2: Analyze the median and mode

For a set to have a mode, a value must repeat. Currently, all values are distinct. If we set $x$ to one of the existing values, it becomes the mode.

Let's test the options to see which value satisfies $\text{Mean}=\text{Mode}=\text{Median}$:

• If $x=10$:

  • Sorted data: $4,6,8,9,10,10,11,15,17$

  • $\text{Mean}=\frac{80+10}{9}=\frac{90}{9}=10$

  • $\text{Mode}=10$

  • $\text{Median}$ (the 5th value) $=10$

  • Since $\text{Mean}=\text{Mode}=\text{Median}=10$, this satisfies the condition.

Correct Option: (b) 10