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If the average (arithmetic mean) of 9 numbers is 43

This topic has 1 expert reply and 0 member replies

If the average (arithmetic mean) of 9 numbers is 43

Post Wed Nov 08, 2017 7:46 am
If the average (arithmetic mean) of 9 numbers is 43, what is the standard deviation of them?

1) The smallest number of them is 43
2) The greatest number of them is 43

The OA is D.

How can I calculate the stanadard deviation without knowing all the numbers?

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GMAT/MBA Expert

Post Wed Nov 08, 2017 6:35 pm
Hi VJesus12,

We're told that the average (arithmetic mean) of 9 numbers is 43. We're asked for the standard deviation of the group. While this question requires some specific knowledge about Standard Deviation, you don't actually have to do much math to solve it. To start, it's worth noting that the GMAT will NEVER ask you to calculate the Standard Deviation of a group using the S.D. formula, so that is NOT what this question is actually about.

Standard Deviation is essentially about how 'spread out' a group of numbers is. The more 'spread out' the numbers, the higher the S.D.; the 'closer together' the numbers, the smaller the S.D. When all of the numbers in a group are the SAME, then the S.D. is 0.

1) The smallest number of the group is 43.

Fact 1 tells us that the SMALLEST number in the group is EQUAL to the average. The ONLY way for that to occur is if ALL 9 numbers are the SAME (they're all 43). Thus, the S.D. must be 0.
Fact 1 is SUFFICIENT

2) The greatest number of the group is 43.

Fact 1 tells us that the LARGEST number in the group is EQUAL to the average. The ONLY way for that to occur is if ALL 9 numbers are the SAME (they're all 43). Thus, the S.D. must be 0.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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