Descriptive Statistics - GMAT Quantitative
Card 0 of 476
Data sufficiency question- do not actually solve the question
Find the mean of a set of 5 numbers.
1. The sum of the numbers is 72.
2. The median of the set is 15.
Data sufficiency question- do not actually solve the question
Find the mean of a set of 5 numbers.
1. The sum of the numbers is 72.
2. The median of the set is 15.
Statement 2 does not provide enough information about the mean as it can vary greatly from the median. Statement 1 is sufficient to calculate the mean, because even though it is impossible to calculate the set of numbers, the mean is calculated by dividing the sum by the total number of incidences in the set.
Statement 2 does not provide enough information about the mean as it can vary greatly from the median. Statement 1 is sufficient to calculate the mean, because even though it is impossible to calculate the set of numbers, the mean is calculated by dividing the sum by the total number of incidences in the set.
Compare your answer with the correct one above
How much greater is the average of the integers from 500 to 700 than the average of the integers from 60 to 90?
How much greater is the average of the integers from 500 to 700 than the average of the integers from 60 to 90?
In this case, average is also the middle value.
In this case, average is also the middle value.
Compare your answer with the correct one above
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.
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.
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.
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.
Compare your answer with the correct one above
What is the median of the following numbers?
Statement 1: 
Statement 2: 
and 
What is the median of the following numbers?
Statement 1:
Statement 2:
Statement 1 alone would not be helpful.
Example 1: If 
and 
, the list, in descending order, is 
and the median would be 
.
Example 2: If 
and 
, the list, in descending order, is 
and the median would be 
.
In contrast, if Statement 2 is true, since 
and 
, 
and 
. Regardless of their relationship, this makes 
the fourth-highest number, and, therefore, the median.
Statement 1 alone would not be helpful.
Example 1: If
Example 2: If
In contrast, if Statement 2 is true, since
Compare your answer with the correct one above
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.
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.
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.
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.
Compare your answer with the correct one above
Given five distinct positive integers - 
- which of them is the median?
Statement 1: 
Statement 1: 
Given five distinct positive integers -
Statement 1:
Statement 1:
Assume Statement 1 alone. By the Addition Property of Inequality, if
,
then 
can be added to each quantity to give an equivalent inequality:
.
By extension, the continued inequality in Statement 1 is equivalent to
.
A similar argument holds for Statement 2. By the Multiplication Property of Inequality, if
, then
and 
.
By extension, the continued inequality in Statement 2 is also equivalent to
.
The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. Therefore, it can be established from either statement alone that of the five, the median is 
.
Assume Statement 1 alone. By the Addition Property of Inequality, if
then
By extension, the continued inequality in Statement 1 is equivalent to
A similar argument holds for Statement 2. By the Multiplication Property of Inequality, if
and
By extension, the continued inequality in Statement 2 is also equivalent to
The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. Therefore, it can be established from either statement alone that of the five, the median is
Compare your answer with the correct one above
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?
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?
Median of A = 3
Mean of A = 3.2
Median of B = 5
Mean of B = 4.8
Median of A = 3
Mean of A = 3.2
Median of B = 5
Mean of B = 4.8
Compare your answer with the correct one above
The median of the numbers 
, 
, 
, and 
is 
. What is 
equal to?
The median of the numbers
The four numbers 
appear in ascending order, so their median 
must be the arithmetic mean of the middle two numbers. Therefore,
The four numbers
Compare your answer with the correct one above
What is the median of a data set comprising nineteen elements?
Statement 1: When arranged in ascending order, the ninth element is 72.
Statement 2: When arranged in descending order, the ninth element is 72.
What is the median of a data set comprising nineteen elements?
Statement 1: When arranged in ascending order, the ninth element is 72.
Statement 2: When arranged in descending order, the ninth element is 72.
In a data set of 19 elements, 19 being odd, the median is the element that occurs in the 
position when they are arranged in ascending (or descending) order. Neither statement alone tells us what that middle element is. But put together, they tell us what the ninth and eleventh elements would be when arranged in ascending (or descending) order. Since both are 72, the element between them - the tenth element, and, thus, the median - must be 72.
The answer is that both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.
In a data set of 19 elements, 19 being odd, the median is the element that occurs in the
The answer is that both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.
Compare your answer with the correct one above
Given five distinct positive integers - - which of them is the median?
Statement 1: 
Statement 2: 
Given five distinct positive integers -
Statement 1:
Statement 2:
Assume Statement 1 alone. The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. By Statement 1, this number is 
, so the question is answered.
Statement 2 alone, however, gives that the mean is 
. It is possible that the mean and the median can be one and the same or two different numbers.
Case 1: 
The mean is
making this consistent with Statement 2.
The median is the middle element, 
.
Case 2: 
again, making this consistent with Statement 2.
The median is the middle element, 
.
Assume Statement 1 alone. The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. By Statement 1, this number is
Statement 2 alone, however, gives that the mean is
Case 1:
The mean is
making this consistent with Statement 2.
The median is the middle element,
Case 2:
again, making this consistent with Statement 2.
The median is the middle element,
Compare your answer with the correct one above
Given five distinct positive integers - - which of them is the median?
Statement 1: 
Statement 2: 
Given five distinct positive integers -
Statement 1:
Statement 2:
Both statements can be shown to be equivalent to the continued inequality
by way of the Multiplication Property of Inequality. We will demonstrate this as follows:
Multiply each expression in
(Statement 1)
by 
:
.
Multiply each expression in
(Statement 2)
by 
:
The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. Therefore, it can be established from either statement alone that of the five, the median is 
.
Both statements can be shown to be equivalent to the continued inequality
by way of the Multiplication Property of Inequality. We will demonstrate this as follows:
Multiply each expression in
(Statement 1)
by
Multiply each expression in
(Statement 2)
by
The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. Therefore, it can be established from either statement alone that of the five, the median is
Compare your answer with the correct one above
What is the mode of a data set with ten data values?
-
The value 15 occurs four times in the data set.
-
The value 16 occurs three times in the data set.
What is the mode of a data set with ten data values?
-
The value 15 occurs four times in the data set.
-
The value 16 occurs three times in the data set.
If we are given only that 15 occurs four times in the data set, it is possible that another number can occur up to six times; similarly, if we are given only that 16 occurs three times, it is possible that another number can occur up to seven times. Either way, the mode - the most frequently occurring data value - cannot be determined.
However, if we know both facts, then no other data value can occur more than three times, so 15 must be the mode.
Therefore, the answer is that both statements are sufficient, but not one alone.
If we are given only that 15 occurs four times in the data set, it is possible that another number can occur up to six times; similarly, if we are given only that 16 occurs three times, it is possible that another number can occur up to seven times. Either way, the mode - the most frequently occurring data value - cannot be determined.
However, if we know both facts, then no other data value can occur more than three times, so 15 must be the mode.
Therefore, the answer is that both statements are sufficient, but not one alone.
Compare your answer with the correct one above
What is the value of 
in the list above?
(1) 
(2) The mode of the numbers in the list is 
.
What is the value of
(1)
(2) The mode of the numbers in the list is
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.
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.
Compare your answer with the correct one above
What is the value of 
in the list of numbers above?
(1) 
.
(2) The mode of the numbers in the list is 
.
What is the value of
(1)
(2) The mode of the numbers in the list is
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
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
Compare your answer with the correct one above
What is the value of 
in the list of numbers above?
(1) The mode of the numbers in the list is 
.
(2) 
.
What is the value of
(1) The mode of the numbers in the list is
(2)
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.
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.
Compare your answer with the correct one above
What is the sum of 
and 
?
(1) The mode of the numbers in the list is 
.
(2) The product of 
and 
is 
.
What is the sum of
(1) The mode of the numbers in the list is
(2) The product of
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.
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.
Compare your answer with the correct one above
Find the mode of the following set of numbers:
Find the mode of the following set of numbers:
The mode is the number that occurs most frequently. Therefore, our answer is 
.
The mode is the number that occurs most frequently. Therefore, our answer is
Compare your answer with the correct one above
Is 3 the average of a sequence？
(1)There are 3 numbers in the sequence
(2)The mode of the sequence is 3
Is 3 the average of a sequence？
(1)There are 3 numbers in the sequence
(2)The mode of the sequence is 3
For statement (1), since we don’t know the value of each number, we cannot calculate the average of the sequence. For statement (2), the mode of the sequence is 3 means that “3” occurs most times in the sequence, but we cannot get to the average because we don’t know the value of other numbers. If we look at the two conditions together, we will know that there are 2 or 3 “3”'s in the sequence, but we don’t know exactly how many times “3” occurs. If the 3 numbers are all “3”s, then we can answer the question; If not, then we cannot answer the question. Thus both statements together are not sufficient.
For statement (1), since we don’t know the value of each number, we cannot calculate the average of the sequence. For statement (2), the mode of the sequence is 3 means that “3” occurs most times in the sequence, but we cannot get to the average because we don’t know the value of other numbers. If we look at the two conditions together, we will know that there are 2 or 3 “3”'s in the sequence, but we don’t know exactly how many times “3” occurs. If the 3 numbers are all “3”s, then we can answer the question; If not, then we cannot answer the question. Thus both statements together are not sufficient.
Compare your answer with the correct one above
Calculate the average of the 5 integers.
Statement 1: They are consecutive even integers.
Statement 2: The smallest of the integers is 8 less than the largest of the five integers.
Calculate the average of the 5 integers.
Statement 1: They are consecutive even integers.
Statement 2: The smallest of the integers is 8 less than the largest of the five integers.
We are looking for an average here. Statement 1 tells us we are looking for even consecutive integers such as 2, 4, 6, 8, and 10. Statement 2 tells us the difference between the smallest and largest integer; however, the difference between the largest and smallest of five consecutive even (or odd) integers will ALWAYS be 8, regardless of what 5 consecutive integers we choose; therefore the two statements don't give us enough information to solve for the average.
We are looking for an average here. Statement 1 tells us we are looking for even consecutive integers such as 2, 4, 6, 8, and 10. Statement 2 tells us the difference between the smallest and largest integer; however, the difference between the largest and smallest of five consecutive even (or odd) integers will ALWAYS be 8, regardless of what 5 consecutive integers we choose; therefore the two statements don't give us enough information to solve for the average.
Compare your answer with the correct one above
1. If the arithmetic mean of five different numbers is 50, how many of the numbers are greater than 50?
(1) None of the five numbers is greater than 100.
(2) Three of the five numbers are 24, 25 and 26, respectively.
1. If the arithmetic mean of five different numbers is 50, how many of the numbers are greater than 50?
(1) None of the five numbers is greater than 100.
(2) Three of the five numbers are 24, 25 and 26, respectively.
For statement (1), there are different combinations that satisfy the condition. For example, the five numbers can be 
or the five numbers can be 
. Therefore, we cannot determine how many of the numbers are greater than 
by knowing the first statement.
For statement (2), even though we know three of them, the two unknown numbers can both be greater than 
, or one smaller and one greater. Thus statement (2) is not sufficient.
Putting the two statements together, we know that the sum of the two unknown numbers is
Since none of them is greater than 100, both of them have to be greater than 50. Therefore when we combine the two statements, we know that there are two numbers that are greater than 50.
For statement (1), there are different combinations that satisfy the condition. For example, the five numbers can be
For statement (2), even though we know three of them, the two unknown numbers can both be greater than
Putting the two statements together, we know that the sum of the two unknown numbers is
Since none of them is greater than 100, both of them have to be greater than 50. Therefore when we combine the two statements, we know that there are two numbers that are greater than 50.
Compare your answer with the correct one above