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QOTD # 5 The sum of the annual salaries of the 21 teachers a

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QOTD # 5 The sum of the annual salaries of the 21 teachers a [#permalink] New post 13 Sep 2016, 02:03
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Question Stats:

80% (01:17) correct 19% (01:18) wrong based on 88 sessions
The sum of the annual salaries of the 21 teachers at School X is $781,200. Twelve of the 21 teachers have an annual salary that is less than $37,000.

Quantity A
Quantity B
The average (arithmetic mean) of the annual salaries of the teachers at School X
The median of the annual salaries of the teachers at School X


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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Question: 5
Page: 203
[Reveal] Spoiler: OA

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Re: QOTD # 5 The sum of the annual salaries of the 21 teachers a [#permalink] New post 13 Sep 2016, 02:05
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Explanation

The average of the annual salaries of the 21 teachers is \(\frac{781,200}{21}\) or \(37,200\) By definition, the median of the 21 annual salaries is the 11th salary when the 21 salaries are listed in increasing order. Note that in the question you are given that 12 of the salaries are less than $37,000. Thus, when the 21 salaries are listed in increasing order, the first 12 salaries in the list are less than $37,000. Thus the median of the salaries, which is the 11th salary in the list, is less than $37,000, which is less than the average salary of $37,200.

The correct answer is Choice A.
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Re: QOTD # 5 The sum of the annual salaries of the 21 teachers a [#permalink] New post 02 May 2020, 07:04
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This is simple once you recognize they've given you a LOT of information.

Start with Quantity A:
We know the average salary equals total salary divided by total teachers
$781,000/21 = 37,190. The average salary is a little more than $37,000

Now, Quantity B:
If 12 of the 21 teachers have an annual salary less than 37,000, we know the median has to be less than 37,000.
The median of 21 is the 11th number, which will always be less than 37,000, based on the info given. The median salary is less than $37,000

You can draw it out to understand: (I dropped the 00s to make it easier to see)

36 + 36 + 36 + 36 + 36 + 36 + 36 +36 + 36 + 36 + 36 (median) + 36 + remaining 9 teachers salary above 37,000

So, Quantity B is less than $37,000 and Quantity A is more than $37,000.
Answer is A
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Re: QOTD # 5 The sum of the annual salaries of the 21 teachers a [#permalink] New post 26 May 2020, 17:59
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It might feel like they're giving you too much information to sift through, but you basically need to find the average and the median and then compare them. And you have the information for that.

To find the average:
(781,200) / (21) = 37,200

The median will be the middle value in the set. You've got 21 values in the set, so the median will be the 11th value (10 on each side). You're told that 12 teachers make less than 37K, which means that the greatest value that the median can be is 36,999.

Therefore, the average is greater than the mean. Answer is A.
Re: QOTD # 5 The sum of the annual salaries of the 21 teachers a   [#permalink] 26 May 2020, 17:59
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QOTD # 5 The sum of the annual salaries of the 21 teachers a

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