<p>A list of integers has the property that the average (arithmetic mean), , of the integers is greater than the median, , of the integers. Which of the following must be true?</p>
<p>I More of these integers are greater than than are less than .
II More of these integers are greater than than are less than .
III More of these integers are less than than are greater than .</p>
<p>Can someone explain the answer to this SAT Question of the Day, Collegeboard's answer didn't make entire sense and I wasn't sure if there was an easier way to do it?
It's from January 7, 2011.</p>
<p>You’re missing numbers in the question, so we can’t evaluate it.</p>
<p>oops. </p>
<p>A list of integers has the property that the average (arithmetic mean),a , of the integers is greater than the median, m, of the integers. Which of the following must be true?</p>
<p>I More of these integers are greater than than are less than .
II More of these integers are greater than than are less than .
III More of these integers are less than than are greater than .</p>
<p>they weren’t numbers, they were variables, my bad.</p>
<p>and two of your options are the same</p>
<p>The median, by definition, will have the same amount of numbers on its left and right sides. </p>
<p>And you could have a set like this: </p>
<p>1 1 3 1000</p>
<p>m is 2
a is much greater than m
but there are two numbers to the left of the median (1 and 1) and two numbers to the right of the median (3 and 1000)</p>
<p>It’s not always the amount of numbers - their magnitude also affects the skew. We are given nothing about the relative magnitudes.</p>
<p>None.</p>
<p>So if you’re given these types of problems with a set of integers, it’s okay pick a smaller set of numbers (if it’s odd, pick odd; if it’s even pick even)?</p>
<p>Thanks!</p>
<p>I think that’s a little general, but in most cases, yes. The goal is to find an easy-to-manipulate model of a complex situation. That’s all the SAT Math is testing: your ability to either abstractly reason and solve the problem or to model the problem in a tinier, concrete, manageable microcosm of the given. </p>
<p>So you should approach every problem with an open mind; don’t set these fixed rules because they will not work every time.</p>