Which of the following values, when inserted into the set of \(7\) values (above), will cause the median of the new set

[VJesus12]

\(\{5, 10, 12, 13, 17, 22, 22\}\)

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

Answer: E

Source: EMPOWERgmat

[deloitte247]

If the no. of terms = odd, median = middle term
But if the no. of terms = even, median = average of two terms in the middle
Presently, there are 7 teams which is an odd number. Adding 1 to it will make it 8 which is even.
$$So,\ median=\frac{4th\ term+5th\ term}{2}$$
Presently, the 4th and 5th term is 13 & 17.
So, depending or whether the new term added is greater or lesser than 13, 13 could either be the 4th or 5th term.
Therefore, let the other term = x
$$\frac{13+x}{2}=15$$
$$13+x=30$$
x = 17

[Scott@TargetTestPrep]

\(\{5, 10, 12, 13, 17, 22, 22\}\)

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

Answer: E

Solution:

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.

Alternate Solution:

The median of the set of 7 values is 13 because it is the (7 + 1)/2 = 4th data value when the values are listed in ascending order.

If an additional value x is added to the set, then the median of the 8 values will be the average of the 4th and 5th data values in the set, and we know its value is 15. Thus we have:

(13 + x)/2 = 15

13 + x = 30

x = 17

This shows that if 17 or any value greater than 17 is added to the set, the median will be 15. The only answer choice which satisfies this is E.

Answer: E