Question: Mean and Median of Set T

Comment on Mean and Median of Set T

I think there is a mistake here. In this specific excercise, the mean and median are not the same. Try ordering the values manually and check.
greenlight-admin's picture

There's a nice rule that says:
"In a set where the numbers are equally spaced, the mean will equal the median"
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}

In this question, the set of numbers consists of all integers fro, -24 to 28 inclusive.
In other words, the set = {-24, -23, -22,......25, 26, 27, 28}

Since all of these consecutive integers are equally spaced, it must be the case that the mean = the median.

For more on this, watch:

Wrong. Please do the operation manually. 12 numbers are negative, one is zero, fourteen are positive. I will not get into details, but the mean is 2 and the median is 1. None of the answers is correct. The correct answer (median minus mean) would be one. Do the operation manually and you will see...
greenlight-admin's picture

You're correct to say that the mean = 2. However, the median is not 1.

There are 27 integers in total.
Since we have an odd number of values, the median is the middlemost value. That is, the median will equal one of those 27 values.
Since all of the number are even, the median must be even.
The median is actually 2.

That said, this question is really testing your knowledge of when the mean and median are equal.

Wrong. Here is the entire set T (every even integer greater than -25 and less than -29):

- 24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 -- as you can see we have 12 negative numbers so far
0 (13th number out of 27)
2 4 6 8 10 12 14 16 18 20 22 24 26 28 (14 positive even numbers)

27 numbers total. 13th number is zero, 14th is 2. Thus, the median would be (2+0)/2 which is one. The arithmetic mean is 2. The median (1) minus the mean (2) would be minus one!
greenlight-admin's picture

When there's an odd number of values, the median is the middle value.

You're correct to say there are 27 numbers.
When arranged in ascending order, the middle number is the 14th number.
As you said, the 14th value is 2
So, there are 13 values less than 2, and there are 13 values greater than 2.
So, the median is 2.

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