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The median of six numbers 6, 7, x – 5, x – 3, 17 and 19, in ascending order, is 11. The value of x is:
- a)10
- b)12
- c)15
- d)16
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The median of six numbers 6, 7, x – 5, x – 3, 17 and 19, in ascending...
The median of six number
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= (x−5) + (x−3)/2
= 2x − 8/2
= x − 4
According to Question-
x - 4 = 11
x = 15
Most Upvoted Answer
The median of six numbers 6, 7, x – 5, x – 3, 17 and 19, in ascending...
Understanding the Problem
We need to determine the value of x in the given set of numbers: 6, 7, x – 5, x – 3, 17, and 19. The median of these numbers is stated to be 11.
Finding the Median
Since there are six numbers, the median is the average of the 3rd and 4th numbers when arranged in ascending order. Thus, we need to ensure that the 3rd and 4th numbers average to 11:
- Median = (3rd number + 4th number) / 2 = 11
This implies:
- 3rd number + 4th number = 22
Arranging the Numbers
To find the correct median, we need to express the numbers in ascending order based on the value of x:
- For various values of x, the expressions will change.
Consider Different Cases for x
- When x = 10:
- x – 5 = 5, x – 3 = 7
- Numbers: 5, 6, 7, 10, 17, 19 (Median = (7 + 10) / 2 = 8.5)
- When x = 12:
- x – 5 = 7, x – 3 = 9
- Numbers: 6, 7, 9, 12, 17, 19 (Median = (9 + 12) / 2 = 10.5)
- When x = 15:
- x – 5 = 10, x – 3 = 12
- Numbers: 6, 7, 10, 12, 17, 19 (Median = (10 + 12) / 2 = 11)
- When x = 16:
- x – 5 = 11, x – 3 = 13
- Numbers: 6, 7, 11, 13, 17, 19 (Median = (11 + 13) / 2 = 12)
Conclusion
The only value of x that yields a median of 11 is when x = 15. Thus, the correct answer is option 'C'.
We need to determine the value of x in the given set of numbers: 6, 7, x – 5, x – 3, 17, and 19. The median of these numbers is stated to be 11.
Finding the Median
Since there are six numbers, the median is the average of the 3rd and 4th numbers when arranged in ascending order. Thus, we need to ensure that the 3rd and 4th numbers average to 11:
- Median = (3rd number + 4th number) / 2 = 11
This implies:
- 3rd number + 4th number = 22
Arranging the Numbers
To find the correct median, we need to express the numbers in ascending order based on the value of x:
- For various values of x, the expressions will change.
Consider Different Cases for x
- When x = 10:
- x – 5 = 5, x – 3 = 7
- Numbers: 5, 6, 7, 10, 17, 19 (Median = (7 + 10) / 2 = 8.5)
- When x = 12:
- x – 5 = 7, x – 3 = 9
- Numbers: 6, 7, 9, 12, 17, 19 (Median = (9 + 12) / 2 = 10.5)
- When x = 15:
- x – 5 = 10, x – 3 = 12
- Numbers: 6, 7, 10, 12, 17, 19 (Median = (10 + 12) / 2 = 11)
- When x = 16:
- x – 5 = 11, x – 3 = 13
- Numbers: 6, 7, 11, 13, 17, 19 (Median = (11 + 13) / 2 = 12)
Conclusion
The only value of x that yields a median of 11 is when x = 15. Thus, the correct answer is option 'C'.
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The median of six numbers 6, 7, x – 5, x – 3, 17 and 19, in ascending order, is 11. The value of x is:a)10b)12c)15d)16Correct answer is option 'C'. Can you explain this answer?
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