A 2 min read

OG 2020: Question No. 384

PQID = DS89950.01

7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

1. x > 7
2. The median of the list equals the arithmetic mean of the list.

Source	OG 2020
PQID	DS89950.01
Type	Data Sufficiency
Topic	Number Properties
Sub-Topic	Statistics
Difficulty	Hard

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• A list of numbers = {7, 9, 6, 4, 5, x}

We need to determine

• The median of the list

Now, to determine the median, first thing we need to do is arrange all the elements of the list in ascending/descending order.

Arranging the numbers we know in ascending order, we get {4, 5, 6, 7, 9}. Notice that the position of x is still unknown. So, to determine the median of the list, we need to know the value of x.

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, x > 7.

If we arrange ‘x’ accordingly in the list, then

• Either the list looks like {4, 5, 6, 7, x, 9} OR {4, 5, 6, 7, 9, x}, depending on the value of x.
• In either of the possible cases, the median of the elements is (6 + 7)/2 = 6.5

As we can determine the exact value of the median, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, the median of the list equals the arithmetic mean of the list.

• The arithmetic mean of all the elements = (7 + 9 + 6 + 4 + 5 + x)/6 = (31 + x)/6
• However, we do not know what is the median of the list.

Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 1 individually, this step is not required.

Hence, the correct answer choice is option A.

TAKEAWAYS:

The median of a list of data is the middle value of the list, when arranged in either ascending or descending order.

• If the data has an odd number of elements (n), then the median = (n+1)/2^th   value.

If the data has an even number of elements (n), then median = average of (n/2)^th and (n/2 + 1)^th values.