Consider the data on $ \mathrm{x} $ taking the values $ 0,2,4,8, \ldots ., 2^{\mathrm{n}} $ with frequencies $ { }^{\mathrm{n}} \mathrm{C}_{0},{ }^{\mathrm{n}} \mathrm{C}_{1},{ }^{\mathrm{n}} \mathrm{C}_{2}, \ldots,{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}} $ respectively. If the mean of this data is $ \frac{728}{2^{\mathrm{n}}} $, then $ \mathrm{n} $ is equal to ....... .

Question

Consider the data on $ \mathrm{x} $ taking the values $ 0,2,4,8, \ldots ., 2^{\mathrm{n}} $ with frequencies $ { }^{\mathrm{n}} \mathrm{C}_{0},{ }^{\mathrm{n}} \mathrm{C}_{1},{ }^{\mathrm{n}} \mathrm{C}_{2}, \ldots,{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}} $ respectively. If the mean of this data is $ \frac{728}{2^{\mathrm{n}}} $, then $ \mathrm{n} $ is equal to ....... .,

MARKS App · Accepted Answer

x i (observation) 0 2 2 2 ................ 2 n f i (frequency) C 0 n C 1 n C 2 n ............. C n n x = Σ f i x i Σ f i 0 × C 0 n + 2 × C 1 n + 2 2 × C 2 n . . . . . 2 n × C n n C 0 n + C 1 n + C 2 n . . . . . + C n n = 3 n - 1 2 n = 728 2 n ⇒ 3 n = 3 6 ⇒ n = 6

$x_{i}$ (observation)	0	2	$2^{2}$ ................	$2^{n}$
$f_{i}$ (frequency)	${}^{n}C_{0}$	${}^{n}C_{1}$	${}^{n}C_{2}$ .............	${}^{n}C_{n}$

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