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maths-aptitude: What is the largest value that can be in this sequence?

The mean, unique mode, median and range of 21 positive integers is 21. What is the largest value that can be in this sequence? Also find such a sequence. Note: Given a sequence of numbers a(1), a(2), ... a(n),
* The median of the sequence is the middlemost value in the sequence if n is odd and the average of the two middle values if n is even.
* The mode is the most occurring value in the sequence
* The range is the difference between the largest and the smallest values, i.e. a(n) - a(1).
For example, the sequence 2, 3, 4, 6, 6, 9 has mean = (2 + 3 + 4 + 6 + 6 + 9)/6 = 5, median = (4+6)/2 =5, mode = 6, and range = 9 - 2 = 7.

maths x 2
aptitude x 2
Posted On : 2017-08-26 16:47:48.0
profile Divesh - anyforum.in Divesh
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Let´s start with the solution, as in sequence we have odd number so 11th element will be 21. So initially we can consider the sequence as below

* 10 Numbers, 21, 10 Numbers

Now we need to focus on 10 Numbers set which we can put on both side of 11th element which is 21. In 10 Numbers sequence which is even sequence let´s fix the median as 21, 5th and 6th element we can make it as 21. So 10 Numbers sequence will be:

10 Numbers sequence=4 Numbers, 21, 21, 4 Numbers.

Now Let´s focus on 4 numbers sequence with the range of 21. I think we can form possible 4 Numbers sequence with largest number as 36 and maintaining the range of 21 as follows:

15, 36, 17, 16

Total Sequence now we can write like:

15, 36, 17, 16, 21, 21, 15, 36, 17, 16, 21, 15, 36, 17, 16, 21, 21, 15, 36, 17, 16

As we can see in above series of 21 elements:

* Mean= 441/21=21
* 11th element is 21, Hence the median of the sequence is 21.
* 21 repeated 5 times i.e. highest frequency, Hence mode is 21.
* Max=36, Min=15 Hence range=21.
* Largest value in the sequence is 36.

So this series also can be the solution of the problem. If some one has better approach/solution with larger value than 36. Please share your idea or solution.


Posted On : 2017-08-29 14:20:05
Satisfied : 6 Yes  0 No
profile Rishi Kumar - anyforum.in Rishi Kumar
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