A set of 19 integers has a median of 31 and a range of 51.

Question

A set of 19 integers has a median of 31 and a range of 51. What is the lowest possible value of the smallest integer in the set?

A. 30
B. 6
C. 5
D. -20
E. -21

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Adit_ · Answer

Just take all values from median till the end as 31 and the first value becomes -20, which is lowest.

Answer:  Option D

chloreton · Answer

An easy one, no constraints are given like the avg of all numbers.

We know median is 31. We can assume the largest number to be also 31. 
Since range is 51, the lowest number has to be -20.

Therefore option  D

KRKfan · Answer

Given: 
# of integers in a set: 19
Range of smallest to largest numbers: 51
Median of the set: 31

To find:  Lowest possible value of the set.

To get lowest possible of the a set we can start with an example where the smallest can be Median (-) Range, i.e 31 - 51 =  -20  and the subsequent values from the median to the largest number are one and the same, i.e.  31 .

The set of 19 integers:
 -20,-20,-20,-20,-20,-20,-20,-20,-20,31,31,31,31,31,31,31,31,31,31

Here the  median  is the 10th value i.e.  31  and the  lowest value  is  -20 .

Correct answer is  D .

vasu1104 · Answer

there are total 19 numbers.
median is 31 so 10th number in list has value of 31.

range = 51
max - min = 51

since there is no average given but only range. that means the higher max goes, min goes to same high. and lower the max goes, min goes to same low.
so now here we want min smallest value and for that we need min highest value.
since we are given the median as 31 so the minimum highest value can be 31 but not less than that.

now lets use the equation.
31- min = 51
min = -20

option D

ExpertsGlobal5 · Answer

D is the correct answer choice.  
 
  Video explanation:

https://www.youtube.com/watch?v=Bk-u16p2P3Y

A set of 19 integers has a median of 31 and a range of 51.

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A set of 19 integers has a median of 31 and a range of 51.

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