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# Need help

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Intern
Joined: 25 Jan 2018
Posts: 1

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29 Jan 2018, 22:48
From my understanding, mean = median if,
1. the set consists of evenly spaced numbers
2. if all the members of the set are equal
3. set has just one number

Is there any thing else? In DS type of "is mean = median" questions, what do you have to know to be sure that mean = median?
Math Expert
Joined: 02 Sep 2009
Posts: 52905

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29 Jan 2018, 23:24
1
mrbigball wrote:
From my understanding, mean = median if,
1. the set consists of evenly spaced numbers
2. if all the members of the set are equal
3. set has just one number

Is there any thing else? In DS type of "is mean = median" questions, what do you have to know to be sure that mean = median?

Notice that all three cases are evenly spaced sets (aka arithmetic progression). 2 and 3 are just special cases (2 is an AP with common difference of 0).

Now, for an evenly spaced set (arithmetic progression), the median equals to the mean. Though the reverse is not necessarily true. Consider {0, 1, 1, 2} --> median = mean = 1 but the set is not evenly spaced.
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Intern
Joined: 16 Sep 2017
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30 Jan 2018, 04:38
Bunuel... Could you please elaborate a bit more

Sent from my Moto G (4) using GMAT Club Forum mobile app
Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 689
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04 Feb 2018, 13:33
PraveenChahal wrote:
Bunuel... Could you please elaborate a bit more

Sent from my Moto G (4) using GMAT Club Forum mobile app

An evenly spaced set is a set where the distance between all of the numbers is the same.

For instance, this is an evenly spaced set:

2, 4, 6, 8, 10

It's evenly spaced because each number is 2 greater than the previous one. And the median of the set equals the mean of the set (they're both 6).

This is also an evenly spaced set:

4, 10, 16, 22

Again, the median equals the mean (they're both 13.)

Finally, this is an evenly spaced set:

3, 3, 3, 3, 3, 3

It's technically evenly spaced, because the space between each pair of numbers is 0! And sure enough, the median equals the mean.

So, if you know that a set is evenly spaced, you also know that its median must equal its mean.

But what Bunuel mentioned is that it doesn't go the other way. If you know that the median equals the mean of a set, the set might be evenly spaced. Or it might not.

In other words:

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Re: Need help   [#permalink] 04 Feb 2018, 13:33
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