Average Is NOT the Whole Story

Say your boss walks into Monday's meeting and says the average project last quarter took 10 weeks. Everyone nods. Nobody asks the only question that matters: did most projects take about 10 weeks, or did nine of them take 4 weeks and one take 64? Same average. Completely different quarter.

I watch Test Takers make the Executive Assessment version of that mistake every single week. They see the word "average," they add everything up, they divide, and they feel great. Then the question asks about the median, or the range, or what the average FORCES to be true, and their nice clean number does nothing for them.

Here's my verdict: knowing how to calculate an average is the entry fee. It is NOT the skill being tested.

What the Quant section is really asking

The Quantitative Reasoning section gives you 14 questions in 30 minutes. It mixes Problem Solving (a normal question with five answer choices) and Data Sufficiency (a question where you decide whether the facts you're given are ENOUGH to answer it, without always finding the answer). Each section is scored from 0 to 20, and all three count the same toward your total, according to GMAC's page on the test structure. So Quant is a full third of your score.

Fourteen questions in 30 minutes works out to a little over 2 minutes each, on average. And yes, that average hides the same thing every average hides. Some questions take 40 seconds. Some take 3 minutes. Nobody spends exactly 2 minutes on each one.

Statistics questions on this test rarely ask "what is the mean?" They ask what the mean, median and range let you KNOW. That's a thinking question wearing a math costume. Integrated Reasoning, the section full of tables and graphs, leans on the same ideas.

Three numbers, in plain words

• Mean: add up the numbers, then divide by how many numbers there are. Think of it as the balance point of the list.
• Median: the middle number once you put the list IN ORDER. If the list has an even count, it's the mean of the two middle numbers.
• Range: the biggest number minus the smallest number. It tells you how far apart the two ends are and nothing at all about the middle.

Now stop. Don't read another word until you answer this: if 5 numbers have a mean of 10, what do you actually know about them?

I'll bet your first thought was "they're all around 10." Wrong. You know exactly ONE thing: they add up to 50. They could be 10, 10, 10, 10, 10. They could be 0, 0, 0, 0, 50. The mean tells you the SUM. Write sum = mean × count on your notepad every time you see a mean, and half of these questions open up on their own.

What each number ignores

Every one of these numbers throws information away. Knowing WHAT it throws away is the real skill.

• The median ignores the extremes. Change the 24 in that list to 2,400 and the median is still 12.
• The mean ignores nothing, which is exactly why one huge number drags it around. That same 2,400 would yank the mean from 10 all the way up to 485.2.
• The range ignores everything except the two ends. The three middle numbers could be anything and the range wouldn't budge.

If you can't picture it, sketch it. A quick number line on your notepad does for statistics what a diagram does for shapes, and you already know my feelings on that: draw it, every time.

The mistakes I see most

1. Doing the average in your head. You hold three numbers in memory, lose one, and pick a wrong answer that looked right. INSTEAD: write sum = mean × count on paper the moment you see a mean.
2. Finding the median of an unsorted list. The middle of the list as printed is NOT the median. INSTEAD: rewrite the list in order first, even when it feels obvious.
3. Forgetting the even count. Six numbers have no single middle. INSTEAD: circle the two middle numbers and take their mean.
4. Treating the range as the biggest number. That's how 24 beat 23 above. INSTEAD: write "big minus small" as its own line of notes.
5. Assuming the mean and median match. They only match when the list balances. INSTEAD: on Data Sufficiency, test one lopsided list and one negative number before you call anything sufficient.

Notice that none of these is a "math" problem. Every single one is a note-taking problem or a testing problem. That's good news, because those are habits, and habits are trainable.

Your move today

Before you open another practice set, grab a sheet of paper. Build three lists of five integers that ALL have a mean of 10: one where the median is bigger than 10, one where it's smaller, and one where it's exactly 10. Then write the range of each one. Give yourself five minutes. If you can't finish, don't get down on yourself. That's your data, and now you know exactly what to train.