How do you find the median of 92 and 98? My teacher says it's 89, how can this be?
I know how to find the median of a set of numbers, but finding the median for only two is different, does anyone know how to do this?
-------------------------------------------------------

answers:
Como say: 92___93___94___95___96___97___98
_________________|__________________

95 is median
-
David say: Then your teacher is wrong because the median of 92 and 98 is 95
-
Jeffrey K say: The median is the middle number. Since there are two numbers, there is no actual middle number in your data set. So the median is the average of your numbers.
(92+98)/2 = 95
-
ignoramus say: I would ask him first to give his definition of "median". To my mind it is meaningless when only two numbers are present. It gives no useful information. The question is either meaningless, or stupid.
-
Johnathan say: 89??!! Your teacher messed up. There's no way a median could be lower than the numerical element(s) in a set with the lowest value. Median...think 'middle'.

In a set with an even number of elements in it, the median is the average of the middle two elements. Since you have just those 2 numbers, average the two. The median is 95.
-
Krishnamurthy say: Median of 92 and 98 is 95.
-
Jeffrey say: (92 + 98)/2 = 95
-
ted s say: the teacher is trying to get you (and the class) to challenge the " 89 " answer...do it
-
Marie K say: finding the median is the same, see two numbers in the middle, https://www.mathsisfun.com/median.html
-
llaffer say: I agree with Luca. The median of a set of two numbers is the same as the mean of those two numbers. The median and mean would be 95.

There is no way by definition that the median can be less than the entire set of data.
-
Philomel say: Look up the definition of median. It is the middle of two sets. In this case it is half way between them. 95.
-
JG say: The median is the middle value of a set of numbers. In this case it's the average.
(92+98)/2 = 190/2 = 95
-
paramvenu say: REMEMBER that the value of a measure of central tendency NEVER falls below the SMALLEST item of the data set...
Your teacher is absolutely WRONG
-
oyubir say: I have to disagree with those who said "it is the mean". I know that they are not confusing median and mean, and that they are saying that because there are only 2 values.
But no definition say so.

A median (not THE median) is a value that cut the set of data into two equals part: a value v, such as there as as many values in the set smaller than v, as values in the set bigget than v.

So, any value between 92 and 98 is a median (check definition on any source; for example wikipedia, obviously, but many other)

The TRADITION is, when there is an even number of values in the set, to choose the mean between the two central value. But that is not the definition. The definition is that you can choose.

Median is used precisely when you cannot trust the mean, because law is not necessarily uniform, so you can have extreme, non representative values, in the set. But if the law is not uniform, there is no justification in choosing specifically the mean. For example, if your data set is obviously logarithmic (random, but there are roughly an equal quantities of values of 1 digits, 2 digits, 3 digits, etc), then a better choice for the median of a even number of values, is to choose exp((log(a)+log(b))/2) (aka √(ab) the "geometric mean") where a and b are the two central values.

Note that this debate is not really important: when you compute median, it is usually when you have enough values, and especially enough central value, enough density of values around the median, so that it doesn't really matter which value you choose between the two central values of your set (those two central values are almost the same anyway).
In other words: nobody never compute the median of two values. Reason why even people who perfectly now what a median is give the wrong answer is.



So why do I take time to say this, if it is not important? Because in my view that means that the good answer is ted s one: you are not suppose to come with "the good value" for the median. There are no unique answer to that. It could be 93, 94, 95, 92.1, 97.9, etc.
But your teacher is obvisouly challenging you with "89".

What you are supposed to say is "I can't give a unique answer for the media of 92 and 98, but I can tell you fore sure that there is no way 89 is a possible answer".
Because 89 do not split the set into 2 equals subset. All 2 values of your set are greater than 89. None are smaller. So 89 is not the median.

So in short: don't try to find the median of 92 and 98. Just prove that it is not 89.
(But if your teacher insist that you give a numerical value for the median, then, unless there are other indication to choose a better method, in doubt choose 95. That is everybody always do, despite what I said)
-
Luca say: With just two number the median should be the avarage, so (92+98)/2 = 95, but it's still a weird request to find the median of only 2 numbers, it doesn't really give you any information.
-