Median - GMAT Quantitative
Card 1 of 91
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.
Tap to reveal answer
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.
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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:
Tap to reveal answer
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
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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.
Tap to reveal answer
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.
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Given five distinct positive integers - 
- which of them is the median?
Statement 1: 
Statement 1: 
Given five distinct positive integers -
Statement 1:
Statement 1:
Tap to reveal answer
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
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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?
Tap to reveal answer
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
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The median of the numbers 
, 
, 
, and 
is 
. What is 
equal to?
The median of the numbers
Tap to reveal answer
The four numbers 
appear in ascending order, so their median 
must be the arithmetic mean of the middle two numbers. Therefore,
The four numbers
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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.
Tap to reveal answer
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.
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Given five distinct positive integers - - which of them is the median?
Statement 1: 
Statement 2: 
Given five distinct positive integers -
Statement 1:
Statement 2:
Tap to reveal answer
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,
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Given five distinct positive integers - - which of them is the median?
Statement 1: 
Statement 2: 
Given five distinct positive integers -
Statement 1:
Statement 2:
Tap to reveal answer
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
← Didn't Know|Knew It →
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.
Tap to reveal answer
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.
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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?
Tap to reveal answer
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
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The median of the numbers , , , and is . What is equal to?
The median of the numbers
Tap to reveal answer
The four numbers appear in ascending order, so their median must be the arithmetic mean of the middle two numbers. Therefore,
The four numbers
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Given five distinct positive integers - - which of them is the median?
Statement 1:
Statement 1:
Given five distinct positive integers -
Statement 1:
Statement 1:
Tap to reveal answer
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
← Didn't Know|Knew It →
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.
Tap to reveal answer
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.
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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.
Tap to reveal answer
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.
← Didn't Know|Knew It →
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:
Tap to reveal answer
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
← Didn't Know|Knew It →
Given five distinct positive integers - - which of them is the median?
Statement 1:
Statement 2:
Given five distinct positive integers -
Statement 1:
Statement 2:
Tap to reveal answer
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
← Didn't Know|Knew It →
Given five distinct positive integers - - which of them is the median?
Statement 1:
Statement 2:
Given five distinct positive integers -
Statement 1:
Statement 2:
Tap to reveal answer
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,
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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.
Tap to reveal answer
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.
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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?
Tap to reveal answer
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
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