Yesterday, Integrated Learning posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:
The answer to this data sufficieny question is E (Statements (1) and (2) TOGETHER are NOT sufficient.)
Remember that Standard Deviation is the way the numbers in a list are organized around the average. For example, if you’re given an average of 10 and a standard deviation of 2, you know that most numbers are organized in the range of 8-12, or 6-14, depending on how many standard deviations away from the average we’re talking about. If you were given an average of 200, you could still have a standard deviation of 2, and the numbers would fall in the range of 198-202, or 196-204, also depending on the number of standard deviations. Compare that with an average of 200 and a standard deviation of 15. It’s the same average, but now the numbers are organized much farther way, between 185-215, or 170-230.
From this you should see that standard deviation refers to the dispersion of the numbers, not the actual average, and so given only the standard deviation, we know nothing at all about the average or the numbers used to make that average.
As you learned in the lesson, the formula for standard deviation involves using all the numbers in the given list of numbers. In the case of this problem, the numbers would have to be the company’s earnings each day in January and each day in February.
Statement 1 tells us only what the standard deviation in January was, but tells us nothing about the actual numbers being used. We know that the standard deviation was $2.3 million. But what was the average? It could be $10 million or $200 million, for example, and still have the same standard deviation. It’s not enough to describe what happens in February.
Statement 2 presents the same issue.
We are left with C or E. Since each month has the same standard deviation, does that mean that they will have the same standard deviation together?
That’s what they want you to think, but it’s the other way around completely.
Standard deviation is strict – in order to find it, you MUST have the numbers in the list to figure out the average first, and then the standard deviation.
Since we don’t have the daily company earnings for this company in January and February, we cannot find the standard deviation for that time.
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