GMAT Math : Descriptive Statistics
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Example Questions
Example Question #7 : Dsq: Calculating Mode
What is the value of 
(1)
(2) The mode of the numbers in the list is 
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Statements (1) and (2) TOGETHER are not sufficient.
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Each Statement ALONE is sufficient.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is n. Therefore n is the mode of the numbers in the list.
Only statement (2) is useful in finding the value of n as it states that the mode of the numbers in the list is 16.
Example Question #8 : Dsq: Calculating Mode
What is the value of 
(1) 
(2) The mode of the numbers in the list is 
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Statements (1) and (2) TOGETHER are not sufficient.
Each Statement ALONE is sufficient.
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Each Statement ALONE is sufficient.
The mode is the value that appears most often in a set of numbers. In the list given, the value that appears the most is m. Therefore, m is the mode in the list of numbers given.
(1)
Therefore, 
Statement (1) is sufficient
(2) The mode of the numbers in the list is 6.
Therefore, 
Statement (2) is sufficient
Each Statement ALONE is SUFFICIENT
Example Question #9 : Dsq: Calculating Mode
What is the sum of 
(1) The mode of the numbers in the list is 
(2) The product of 
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Each Statement ALONE is sufficient.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Statements (1) and (2) TOGETHER are not sufficient.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is 2y. Therefore 2y is the mode of the numbers in the list.
(1) The mode of the numbers in the list is 20.
We still don't know the value of x. Statement (1) ALONE is not sufficient.
(2) The product of x and y is 150.
Statement (2) ALONE is not sufficient.
Using both statements, we can write
Therefore,
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Example Question #1201 : Data Sufficiency Questions
Find the mode of the following set of numbers:
The mode is the number that occurs most frequently. Therefore, our answer is 
Example Question #1201 : Data Sufficiency Questions
What is the value of 
(1) The mode of the numbers in the list is 
(2) 
Each Statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are not sufficient.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is m+1. Therefore m+1 is the mode of the numbers in the list.
Only statement (1) is useful in finding the value of m as it states that the mode of the numbers in the list is 14.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Example Question #1 : Dsq: Calculating Median
What is the median number of students assigned per workshop at School R?
(1) 30% of the workshops at School R have 6 or more students assigned to each workshop.
(2) 40% of the workshops at School R have 4 or fewer students assigned to each workshop.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Looking at statements (1) and (2) separately, we cannot get the median number since we don’t know the 50th percentile. However, putting the two statements together, we know that the 50th percentile is 5. So the median is 5.
Example Question #2 : Dsq: Calculating Median
The median of the numbers 
None of the other answers are correct.
The four numbers 
Example Question #3 : Dsq: Calculating Median
What is the mean of this set?
1)
2)
If 
If 
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
Example Question #1 : Dsq: Calculating Median
Data Sufficiency Question
The mean of 8 numbers is 17. Is the median also 17?
1. The range of the numbers is 11.
2. The mode is 17.
statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
each statement alone is sufficient
statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
The range tells us the difference between the maximum and the minimum values, but provides no information about the median. The mode indicates the number that appears most frequently in the data set. While it is possible that the median is 17, it is impossible to determine the median from the data provided.
Example Question #5 : Dsq: Calculating Median
On Monday, 40 people are asked to rate the quality of product A on a seven point scale (1=very poor, 2=poor.....6=very good, 7=excellent).
On Tuesday, a different group of 40 is asked to rate the quality of product B using the same seven point scale.
The results for product A:
7 votes for category 1 (very poor);
8 votes for category 2;
10 votes for 3;
6 vote for 4;
4 votes for 5;
3 votes for 6;
2 votes for 7;
The results for product B:
2 votes for category 1 (very poor);
3 votes for category 2;
4 votes for 3;
6 vote for 4;
10 votes for 5;
8 votes for 6;
7 votes for 7;
It appears that B is the superior product.
Which one of the following statements is true?
The median score of product A is greater than the mean score of product A.
The median score for product A is less than the mean score for product A.
The median score of product A is greater than the median score of product B.
The median score of product B is less than the mean score of product B.
The mean score of product A is greater than the mean score of product B.
The median score for product A is less than the mean score for product A.
Median of A = 3
Mean of A = 3.2
Median of B = 5
Mean of B = 4.8
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