Statistics: Median of a set with an unknown value

Question

Source: Manhattan

Consider the unordered set {x,2,5,11,11,12,33}, No matter whether x is less than 11 ,equal to or greater than 11, the median will ALWAYS BE 11.
While in the unordered set {x,2,5,11,12,12,33}, the median depends on x. If x is 11 or less, median is 11 and if x is between 11 and 12, median is x and finally if x is 12 or more, median is 12

Ques: I did not understand how the statement claims ALWAYS BE 11. Is there a fundamental rule I am missing here? (Though when I try substituting different value, I agree to this statement.)

viv007 · Answer

hi...

simplest way is just put values for x and check, u will find that whatever value you use the median will be always 11.
i hope u clear on this.

ritikajain1988 · Answer

AGREED! But is there a property which I am missing here? Since the author claims as ALWAYS BE??

The author seemed to have intended to say 'As you already know'. ??

TIA!!

push12345 · Answer

Hi ritika

Thing is that in 1st
{x,2,5,11,11,12,33}
We have seven number so median will be fourth one.
11 hold here are there are three number which are less than equal to 11
And there are three number which are greater than equal to 11
So 11 will always be median in this case

In 2nd one
{x,2,5,11,12,12,33}
In this case seven number,again median will be 4th term
Here 3 numbers are less than equal to 12 
But 3 numbers are not greater than equal to 12 
So value of median depend on value of x which determines that value as median which has three number less than equal to it and three numbers greater than equal to this

Hope this helps
Give kudos if it does

Posted from my mobile device

foryearss · Answer

There is no rule to know whether the median will ALWAYS be the same or it will depend on x , other than by noticing and experimenting and seeing the result .

ccooley · Answer

Good question!

Take a look at the values you already know:

2 5 11 11 12 33

You know six of the seven values. Since there are seven values, including the unknown one, the median will always be the 'middle' value - the one that's fourth in line.

No matter where you put 'x' in the list, the number 11 will always be 4th in line. For instance, if x is a small number, it would go towards the beginning of the list:

2  3  5 11 11 12 33

and the number 11 is fourth.

If x is a large number, it would go towards the end of the list:

2 5 11 11 12  30  33

and the number 11 is still fourth.

This only really works because there are two copies of the number 11 in the list, and those two copies are already pretty much in the middle of the list. Adding a new number to the list will only move the median up or down slightly. For instance, the median in a 6-number list is the average of number 3 and number 4. The median in a 7-number list is number 4. That's only a very small change. If number 3 and number 4 were already equal, then the median won't change at all.

Statistics: Median of a set with an unknown value

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