{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
{5, 10, 12, 13, 17, 22, 22} Which of the following values,
This topic has expert replies
-
- Legendary Member
- Posts: 1622
- Joined: Thu Mar 01, 2018 7:22 am
- Followed by:2 members
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let's test each answer choice....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
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
Cheers,
Brent
-
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
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
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7249
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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.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
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich