Consider the data on taking the values with frequencies respectively. If the mean of this data is , then is equal to ........ .

Question

Consider the data on  taking the values  with frequencies  respectively. If the mean of this data is , then  is equal to ........ .

Canvas Classes · Accepted Answer

🧠 Frequencies Are Binomial — Reach for the Binomial Theorem

Look at the frequencies: . Whenever you see binomial coefficients as frequencies, your first thought should be: the sum , and the weighted sum . So if the data values follow some pattern like , the numerator of the mean collapses into . Half the problem is gone before any algebra.

Now look at the values: . The first value is  (not ), and the rest are . So the values are  for , with a  at . We will use this carefully.

🗺️ Working It

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