JEE Main 2025 — Statistics Question with Solution

Let’s set up two equations from the given mean and variance:

Mean = 9 ⇒ total sum = 8·9 = 72

Known values sum to 6+4+8+12+10+13 = 53, so

$$a+b=72-53=19.$$

Population variance = 9.25 ⇒

$$\frac{\sum x_i^2}{8}-9^2=9.25⟹\sum x_i^2=8(81+9.25)=722.$$

Known squares sum to 6²+4²+8²+12²+10²+13² = 529, so

$$a^2+b^2=722-529=193.$$

Now use

$$(a+b{)}^2=a^2+2ab+b^2⟹19^2=193+2ab$$

so

$$361=193+2ab⟹ab=84.$$

Finally,

$$a+b+ab=19+84=103.$$

Answer: 103 (Option A).