Need help

Question

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?

Bunuel · Answer

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.

PraveenChahal · Answer

Bunuel... Could you please elaborate a bit more

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

ccooley · Answer

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:

https://i.imgur.com/lewxAhZ.png

Need help

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards