Which of the following values, when inserted into the set of 7 values

Question

{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

QUANT 4-PACK SERIES Problem Solving Pack 2 Question 1 Which of the following values...

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musunna · Answer

Concept of Median  
Median is the middle number of a sorted distribution. In case of even number of items, Median will be the average of middle two values.

The question asks for   a new number that will cause the median of new set at 15.
Mentionable that given set is already sorted and number of items of new set will be 7+1 = 8.

To get median 15,  the sum of 4th & 5th Term should be 30  and luckily  it's exactly same in the existing series i.e. 13+17.

So to keep the median 15,  the new item should be >=17 .

Thus correct option (E)

ENGRTOMBA2018 · Answer

For the new number to push the median of a set with 8 elements to 15 ---> average of the 4th and the 5th term with the new element = 15

New set's 4th term = 13

Thus, (13+x)/2=15 ---> x = 17.

E is the correct answer.

longfellow · Answer

The answer is 17. As the number of terms of new set will be even, median=mean of middle terms. one term is 13 so other becomes 17.

EMPOWERgmatRichC · Answer

Hi All,

The GMAT will ask a few questions that involve statistical vocabulary and concepts (mean, median, mode, range, standard deviation), so it's important to know all of the basic rules regarding these terms.

To start, we're given a set of 7 terms (and the terms are in order from least-to-greatest, which is quite helpful). We're asked to input an 8th term so that the median of the new set becomes 15.

When a set has an ODD number of terms, the median is the 'middle' number. In a set of 7 numbers arranged from least to greatest, that would make the 4th term the median.

When a set has an EVEN number of terms though, there is no "middle" number, so the median is the AVERAGE of the 'two middle' numbers. With a set of 8 terms, that would be the average of the 4th and 5th terms. Since the current 'middle term' of the set is 13, we need to include a LARGER number to increase the median...

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

Final Answer:  E

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

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Which of the following values, when inserted into the set of 7 values

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GMAT Problem Solving (PS) Questions

Which of the following values, when inserted into the set of 7 values

Prep Toolkit

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