The 'Symmetric Sequence' Trick for Standard Deviation

As a 99th percentile instructor, I've seen countless students grapple with the Quantitative section, especially when they encounter terms that sound intimidating. Two such terms that often trip up test-takers are "symmetric sequence" and "standard deviation." But what if I told you that, for exams such as GMAT, GRE, CAT and SAT these concepts are far simpler than they appear?

Let me walk you through a classic Quant problem to show you how you can tackle it with confidence, just like my most successful students do.

Key Concept 1: The Power of a "Symmetric Sequence"

This is the first major clue. When a sequence is defined as "symmetric about the mean," it simply means the values are perfectly balanced on either side of the average.

Here's my crucial insight: For any symmetric sequence, the mean is always equal to the median. This means the mean (m) sits at the exact center, representing the 50% mark of all values.

Key Concept 2: Unpacking "Standard Deviation"

When you hear "one standard deviation away," simply think of it as "one step or one leap" from the mean. The problem states that "68% of the values are within one standard deviation." Since the distribution is symmetric, this 68% is split perfectly:

• 34% of the data lies between the mean (m) and one step above it (m+d).
• The other 34% lies between the mean (m) and one step below it (m-d).

Putting It Together

Follow the steps on the interactive number line below to see my method in action.

And just like that, a seemingly complex Quant problem becomes a straightforward calculation! Remember, mastering these fundamental interpretations is key to acing the Quant section on GMAT, GRE, CAT and SAT. Keep practicing, and you'll soon find these challenging questions becoming your strongest assets!