Let x₁, x₂, x₃,, x₂₀ be in geometric progression with x₁=3 and the common ratio 1/2. A new data is constructed replacing each x i by (x i -i)². If x is the mean of new data, then the greatest integer less than or equal to x is _ _ _ _ _ _.

Statistics and Probability: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jul, Morning shift · Q51

JEE Main 202228 Jul, Morning shiftMathematicsMediumStatistics and Probability258× since 2002

Let

x_{1}, x_{2}, x_{3}, \ldots, x_{20}

be in geometric progression with

x_{1}=3

and the common ratio

\frac{1}{2}

. A new data is constructed replacing each

x_{i}

\left(x_{i}-i\right)^{2}

. If

\bar{x}

is the mean of new data, then the greatest integer less than or equal to

\bar{x}

is ____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 Statistics and Probability Question with Answer (28 Jul Morning shift, Q51) | JEE Arc