Consider the data on x taking the values 0,2,4,8,…,2n with frequencies (0n),(1n),(2n),…,(nn) respectively. If the mean of this data is 2n728, then n is equal to \_\_\_\_\_\_\_.
Answer: 6
Solutions · 1
Official solution
\[\text{Mean} = \frac{0\cdot\binom n0+2\cdot\binom n1+2^2\binom n2+\cdots+2^n\binom nn}{\binom n0+\binom n1+\cdots+\binom nn}\]
Using (1+x)n with x=2: numerator's non-constant part relates to 3n−1; denominator =2n.
\[\frac{3^n-1}{2^n} = \frac{728}{2^n} \implies 3^n=729 \implies n=6\]