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?
- x > 7
- 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)/2th value.
If the data has an even number of elements (n), then median = average of (n/2)th and (n/2 + 1)th values.
