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ian7777
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An Olympic diver received the following scores: 6.0, 5.5, Updated on: 22 Jun 2015, 02:23
Originally posted by ian7777 on 28 Jun 2007, 12:41.
Last edited by Bunuel on 22 Jun 2015, 02:23, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

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85% (01:10) correct 15% (01:11) wrong based on 48 sessions

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An Olympic diver received the following scores: 6.0, 5.5, 7.0, 6.5, and 5.0. The standard deviation of her scores is in which of the following ranges?

A. 0 – 1.9
B. 2 – 3.9
C. 4 – 6.9
D. 7 – 7.9
E. 8 – 9.9

Hint: Don't use the SD formula.

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A
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Himalayan
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An Olympic diver received the following scores: 6.0, 5.5, 28 Jun 2007, 12:46
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ian7777
An Olympic diver received the following scores: 6.0, 5.5, 7.0, 6.5, and 5.0. The standard deviation of her scores is in which of the following ranges?

A) 0 – 1.9
B) 2 – 3.9
C) 4 – 6.9
D) 7 – 7.9
E) 8 – 9.9

Hint: Don't use the SD formula.
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got A but do not know how to find SD without using formula.

has it anything with the difference of each scores i.e. 0.5?

help needed.
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andrehaui
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An Olympic diver received the following scores: 6.0, 5.5, 28 Jun 2007, 12:54
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I go by logic if the distance form smallest number to highest number is 2, the SD would be on the alternative A range 0-1.9
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An Olympic diver received the following scores: 6.0, 5.5, 28 Jun 2007, 12:57
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What's the SD formula? It's not for me...but for a buddy of mine who can't remember... :P
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An Olympic diver received the following scores: 6.0, 5.5, 28 Jun 2007, 13:04
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Since the average is 6 - then:

SD of 6 is zero.

SD of 5 and 7 = opposite diraction = zero (cancel each other).

SD of 5.5 and 6.5 = opposite diraction = zero (cancel each other).

the answer is (A)

the SD is zero !

:-D
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An Olympic diver received the following scores: 6.0, 5.5, 28 Jun 2007, 13:11
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KillerSquirrel
Since the average is 6 - then:

SD of 6 is zero.

SD of 5 and 7 = opposite diraction = zero (cancel each other).

SD of 5.5 and 6.5 = opposite diraction = zero (cancel each other).

the answer is (A)

the SD is zero !

:-D
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:-D That's a nice try, but no. Remember, standard deviation gives us an idea of how far the numbers vary/deviate from the average. If all numbers were 6: 6, 6, 6, 6, 6, there would be no deviation, and the average would be 6, SD = 0.

We have numbers that go like this: 5, 5.5, 6, 6.5, 7. So there most definitely is deviation. But do we need a formula to see that no number deviates more than 1 away from the average? Not in this case. We could guess that the SD would really be about .8, somewhere between .5 and 1.

In fact, there's no way the SD could be higher than 1 - the range in A is overly generous.

So andrehaui's response is close, but we really only care about the range from the outer number to the average.
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An Olympic diver received the following scores: 6.0, 5.5, 28 Jun 2007, 13:12
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KillerSquirrel
Since the average is 6 - then:

SD of 6 is zero.

SD of 5 and 7 = opposite diraction = zero (cancel each other).

SD of 5.5 and 6.5 = opposite diraction = zero (cancel each other).

the answer is (A)

the SD is zero !

:-D
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Killer,

it cannot be zero because squares of mean deviations are +ve. therefore they can not be cancelled out. but it is less than 1.9.
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An Olympic diver received the following scores: 6.0, 5.5, 28 Jun 2007, 13:19
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ian7777
KillerSquirrel
Since the average is 6 - then:

SD of 6 is zero.

SD of 5 and 7 = opposite diraction = zero (cancel each other).

SD of 5.5 and 6.5 = opposite diraction = zero (cancel each other).

the answer is (A)

the SD is zero !

:-D

:-D That's a nice try, but no. Remember, standard deviation gives us an idea of how far the numbers vary/deviate from the average. If all numbers were 6: 6, 6, 6, 6, 6, there would be no deviation, and the average would be 6, SD = 0.

We have numbers that go like this: 5, 5.5, 6, 6.5, 7. So there most definitely is deviation. But do we need a formula to see that no number deviates more than 1 away from the average? Not in this case. We could guess that the SD would really be about .8, somewhere between .5 and 1.

In fact, there's no way the SD could be higher than 1 - the range in A is overly generous.

So andrehaui's response is close, but we really only care about the range from the outer number to the average.
Show more


:oops:

Actually I wanted to deled my post as soon as I posted it (and understood that my answer is wrong) but you were faster. :wink:

In SD formula all the numbers are in the power of two so they can't be cancel out.

thanks - ian7777 & Himalayan

:-D
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An Olympic diver received the following scores: 6.0, 5.5, 21 Jun 2015, 18:01
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Bunuel can you Please solve and post the Official answer.
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An Olympic diver received the following scores: 6.0, 5.5, 21 Jun 2015, 18:35
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Hi honchos,

The GMAT will test you on your basic understanding of the 'concepts' behind Standard Deviation, but you'll never be asked to actually calculate it. Here, you should notice that the answer choices are RANGES, so super-accuracy is NOT required. Instead, think about the ideas behind SD....

The average of this group of numbers will be something between the lowest value (5.0) and the highest value (7.0) - it's not hard to see that the actual average is 6, but you don't have to know that exact number to answer the question. The Standard Deviation relates to the average, but CANNOT be equal to or greater than the range of the numbers involved. Here, the range is 7-5 = 2, so the SD would have to be LESS than that...

There's only one answer that fits....

Final Answer:
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A

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An Olympic diver received the following scores: 6.0, 5.5, 17 Nov 2024, 22:22
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