PriyankaGmatIMD
Can someone help me understand this... Even after reading it multiple times , i just donot understand this
It states that given set has 50 different integers. And statement 1 gives 2 details that median = 50 and range = 50.
If median is 50 for a set with even number of integers then middle 2 integers need to be 49 and 51 to minimize the range of the set because selecting any other pair would by default increase the overall range, which means you have 24 integers less than 49 and 24 integers greater than 51.
Now you are given that range is 50, which means highest number - lowest number = 50. so if you pick all 24 consecutive numbers below 49 (25, 26, 27, ...., 48, 49) it will give you 25 integers which is the first half of the set and if you pick all 24 consecutive numbers above 51 (51,52,53, ...., 74,75) it will give you 25 integers which is the second half of the set, you will get an exact range of 50(highest - lowest = 75 - 25 = 50).
This is the optimal selection of 24 integers both below and above the numbers pivoted around median. If we lower our lower limit or increase our upper limit, you can verify that range constraint won’t match. Hence this selection would be the only optimal and unique selection for the given constraints.