Consider the data on x taking the values 0,2,4,8, ..., 2? with frequencies ?C?, ?C?, ?C?, ..., ?C? respectively. If the mean of this data is 728/2?, then n is equal to

x? = Σf? x? / Σf?
Σf? =? C? +? C? +? C? + . +? C? = 2?
Σf? x? = (0 ×? C? ) + (2 ×? C? ) + (2² ×? C? ) + . + (2? ×? C? )
This sum is Σ? ? C? 2? = (Σ? ? C? 2? ) -? C?2? = (1+2)? - 1 = 3? - 1.
x? = (3? - 1)/2?
Given x? = 728 / (something that resolves to 2? ). Assuming it is 728/2?
(3? - 1)/2? = 728/2?
⇒ 3? - 1 = 728
⇒ 3? = 729
⇒ 3? = 3?
⇒ n = 6

<div class="photo-widget-full"><div class="figure"><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1756472641php9WJqh1.jpeg" alt="" width="343" height="85" loading="lazy"></picture></div></div><p>x? = Σf? x? / Σf? <br>Σf? =? C? +? C? +? C? + . +? C? = 2? <br>Σf? x? = (0 ×? C? ) + (2 ×? C? ) + (2² ×? C? ) + . + (2? ×? C? )<br>This sum is Σ? ? C? 2? = (Σ? ? C? 2? ) -? C?2? = (1+2)? - 1 = 3? - 1.<br>x? = (3? - 1)/2? <br>Given x? = 728 / (something that resolves to 2? ). Assuming it is 728/2? <br> (3? - 1)/2? = 728/2? <br>⇒ 3? - 1 = 728<br>⇒ 3? = 729<br>⇒ 3? = 3? <br>⇒ n = 6</p></div></div>

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