Question

Consider the set of all four-digit positive integers less than 2000 whose digits have a sum of 24. What's the median of this set?

Answer 1

Answer:

The set of all four-digit positive integers less than 2000 whose digits have a sum of 24 is {1599, 1689, 1698, 1779, 1797, 1869, 1896, 1959, 1968, 1977, 1986, 1995}.

Median states that the value for which half the numbers are larger and half are smaller. If there are two middle numbers, then the median is the arithmetic mean of the two middle numbers.

Since the set contains 12 number of terms which is even, therefore  the two middle terms are 1869 and 1896 then the median is the arithmetic mean of these numbers i.e,  $\frac{1869+1896}{2}=1882.5$

Therefore, the median of the above set is, 1882.5