Consider a data set that consists of positive integers less than 51. There is ex

Question

Consider a data set that consists of positive integers less than 51. There is exactly one 1 in the data set, and every other integer appears twice as many times as its predecessor appears (so there are exactly two 2s, exactly four 3s, exactly eight 4s, exactly sixteen 5s, etc.) what is the median of this data set? Consider a data set that consists of positive integers less than 51. There is exactly one 1 in the data set, and every other integer appears twice as many times as its predecessor appears (so there are exactly two 2s, exactly four 3s, exactly eight 4s, exactly sixteen 5s, etc.) what is the median of this data set?

Explanation / Answer

Observe the sequence 1, 2, 4, 8, 16 ....

We have by the formula for G.P or otherwise, the n + 1 th term as

tn = 2n

We also have by the sum of GP formula, sum to n terms as

(2n - 1)

Thus the n + 1 th term is greater than the sum to n terms.

As a result, in the given question, the mid point falls to the last group.

For e.g if the set is 1,2,2,3,3,3,3, since 3,3,3,3 is the last group, the median is 3.

Thus the median is the greatest integer in the set.

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