Problem with one of the questions in practice test

[tanviarora087]

Hi

While writing one of your tests, I came across this question:
"The 30 people in town A range from 17 to 57 years old with a standard deviation of 4. The 20 people in town B range from 16 to 58 years old with a standard deviation of 6."

But I am unable to understand the explanation. Would you please elaborate the solution?

[tommywallach]

Hey Tanvia,

You haven't actually written out the question here. Please write the rest of the question, so we can all see it.

Thanks!

-t

[choroksallychung]

Hi Tommy, I believe the question is included in the post. Would you be able to help clarify the explanation? This is a QC question 5 out of 20 in one of the quant sections in the practice exams.

Question: The 30 people in town A range from 17 to 57 years old with a standard deviation of 4. The 20 people in town B range from 16 to 58 years old with a standard deviation of 6.

Quantity A

Average age of Town A

Quantity B

Average age of Town B

Explanation: The average age in Town B will be either younger or older than Town A, but we cannot tell which one. If you look at the addition of the squared differences, Town A’s total sum of squared differences is 480 and Town B’s is 720. But in Town B, you can create a case for both an average age of less than that for Town A and greater than that for Town A. It all depends on the actual ages in each town. Though the differences between the mean and individual ages in town B is greater, we cannot determine if the average age is greater than or less than the average age in town A.

This problem provides almost enough information to start working with numbers. If you recognize that standard deviation only measures the squared distance from the mean, then you will see that you cannot determine the mean.

[tommywallach]

I would explain this WAY more simply. Standard deviation is a measurement of how spread out the numbers are in a given set. It doesn't actually tell you WHERE they are...just how spread out.

In this case, you have similar ranges for both towns, and similar SD's (4 and 6 are relatively close). This simply doesn't tell you anything about the average, because to know the average, you'd have to add up all the ages and divide by the number of people, something we can't do with this info.

-t