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{5, 10, 12, 13, 17, 22, 22} Which of the following values,

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by Brent@GMATPrepNow » Sat Nov 23, 2019 6:56 am
Gmat_mission wrote:{5, 10, 12, 13, 17, 22, 22}

Which of the following values, when inserted into the set of 7 values (above), will cause the median of the new set to become 15?

A) 2
B) 11
C) 15
D) 16
E) 17
Let's test each answer choice....

A. 2
The new set becomes {2, 5, 10, 12, 13, 17, 22, 22}
Since we have an EVEN number of values in the set, the median equals the average of the two middlemost numbers.
So, median = (12 + 13)/2 = 25/2 = 12.5
No good - we want the median to be 15

B. 11
The new set becomes {5, 10, 11, 12, 13, 17, 22, 22}
Median = (12 + 13)/2 = 25/2 = 12.5
No good - we want the median to be 15

.
.
.

E. 17
The new set becomes {5, 10, 12, 13, 17, 17, 22, 22}
Since we have an EVEN number of values in the set, the median equals the average of the two middlemost numbers.
So, median = (13 + 17)/2 = 30/2 = 15
Bingo!

Answer: E

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Brent
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by deloitte247 » Fri Nov 29, 2019 6:43 am
When the sample or observation in a given set of data or population is odd, then median = data in the middle when arranged in ascending order.
But if the sample is even, then the median = average of the 2 values or data in the middle when arranged in ascending order.
By adding another data to the existing values, the number of data becomes even.

Median = y/2 where y is the sum of two data in the middle when arranged in ascending order and median = 15

15 = y/2 y = 15 * 2 = 30
Median of old set = 13

For the new set =>y1 + y2 = 30 where y = 13
=> 13 + y2 = 30
y2 = 30 - 13
y2 = 17

17 needs to be added so that median = 15

Answer = option E
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by Scott@TargetTestPrep » Sun Dec 08, 2019 7:38 pm
Gmat_mission wrote:{5, 10, 12, 13, 17, 22, 22}

Which of the following values, when inserted into the set of 7 values (above), will cause the median of the new set to become 15?

A) 2
B) 11
C) 15
D) 16
E) 17

[spoiler]OA=E[/spoiler]

Source: EMPOWERgmat
When 17 is added to the list, we now have 8 data values. When a data set has an even number of data values, the median is the average of the two middle values. Thus, the new median is (17 + 13)/2 = 30/2 = 15.

Answer: E

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answer

by [email protected] » Mon Dec 09, 2019 3:40 pm
Hi Gmat_mission,

We're given the set: {5, 10, 12, 13, 17, 22, 22}

and we're asked which of the following values, when inserted into the set of 7 values (above), will cause the median of the new set to become 15. This question can be solved in a number of different ways, including by focusing on the exact definition of the word MEDIAN and doing a little Arithmetic.

To find the MEDIAN of a group of numbers, we first have to put those numbers in order from least to greatest. This initial set of 7 values are already in order - and the MEDIAN is the 'middle number' in the set (in this case, the 4th of the 7 numbers). When we include an 8th number though, the MEDIAN becomes the AVERAGE of the "two middle terms" (re: the average of the 4th and 5th numbers).

To raise the MEDIAN of the new set to 15, we clearly need to place in a number that is LARGER than 13. That 8th number - when AVERAGED with 13 - will equal 15. You can set up the Average Formula:

(X+13)/2 = 15
X+13 = 30
X = 17

Or you might recognize that 13 is 'two less' than 15, so the new number must be 'two more' than 15.... 15+2 = 17. Either way, you have the correct answer.

Final Answer: E

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Rich
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