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The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?
- a)10.0
- b)10.5
- c)11.0
- d)11.5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The arithmetic mean of 11 observations is 11. The arithmetic mean of t...
Sum of numbers = Average of the numbers × Number of observations
Sum of 11 observations = Sum of first 6 numbers + Sum of last 6 number - 6th number [∵ 6th observation is added twice]
11 × 11 = 10.5 × 6 + 11.5 × 6 - 6th number
121 = 63 + 69 - 6th number
∴ 6th number = 132 - 121 = 11
11 × 11 = 10.5 × 6 + 11.5 × 6 - 6th number
121 = 63 + 69 - 6th number
∴ 6th number = 132 - 121 = 11
Most Upvoted Answer
The arithmetic mean of 11 observations is 11. The arithmetic mean of t...
Problem:
The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?
Solution:
To find the sixth observation, we need to determine the sum of all 11 observations and then subtract the sum of the first five and the sum of the last five observations. Let's break down the problem step by step.
Step 1: Find the sum of all 11 observations:
The arithmetic mean of 11 observations is given as 11. We know that the arithmetic mean is calculated by dividing the sum of all observations by the total number of observations. Therefore, the sum of all 11 observations can be found by multiplying the mean (11) by the total number of observations (11).
Sum of all 11 observations = 11 * 11 = 121
Step 2: Find the sum of the first 6 observations:
The arithmetic mean of the first 6 observations is given as 10.5. Similar to Step 1, we can find the sum of the first 6 observations by multiplying the mean (10.5) by the total number of observations (6).
Sum of first 6 observations = 10.5 * 6 = 63
Step 3: Find the sum of the last 6 observations:
The arithmetic mean of the last 6 observations is given as 11.5. Again, we can find the sum of the last 6 observations by multiplying the mean (11.5) by the total number of observations (6).
Sum of last 6 observations = 11.5 * 6 = 69
Step 4: Determine the sixth observation:
To find the sixth observation, we need to subtract the sum of the first 5 observations from the sum of all 11 observations, and then subtract the sum of the last 5 observations.
Sixth observation = (Sum of all 11 observations) - (Sum of first 5 observations) - (Sum of last 5 observations)
Sixth observation = 121 - 63 - 69
Sixth observation = 121 - 132
Sixth observation = -11
Conclusion:
The sixth observation is -11. However, since this is not an option in the given choices, it is likely that there is an error in the question or the choices provided.
The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?
Solution:
To find the sixth observation, we need to determine the sum of all 11 observations and then subtract the sum of the first five and the sum of the last five observations. Let's break down the problem step by step.
Step 1: Find the sum of all 11 observations:
The arithmetic mean of 11 observations is given as 11. We know that the arithmetic mean is calculated by dividing the sum of all observations by the total number of observations. Therefore, the sum of all 11 observations can be found by multiplying the mean (11) by the total number of observations (11).
Sum of all 11 observations = 11 * 11 = 121
Step 2: Find the sum of the first 6 observations:
The arithmetic mean of the first 6 observations is given as 10.5. Similar to Step 1, we can find the sum of the first 6 observations by multiplying the mean (10.5) by the total number of observations (6).
Sum of first 6 observations = 10.5 * 6 = 63
Step 3: Find the sum of the last 6 observations:
The arithmetic mean of the last 6 observations is given as 11.5. Again, we can find the sum of the last 6 observations by multiplying the mean (11.5) by the total number of observations (6).
Sum of last 6 observations = 11.5 * 6 = 69
Step 4: Determine the sixth observation:
To find the sixth observation, we need to subtract the sum of the first 5 observations from the sum of all 11 observations, and then subtract the sum of the last 5 observations.
Sixth observation = (Sum of all 11 observations) - (Sum of first 5 observations) - (Sum of last 5 observations)
Sixth observation = 121 - 63 - 69
Sixth observation = 121 - 132
Sixth observation = -11
Conclusion:
The sixth observation is -11. However, since this is not an option in the given choices, it is likely that there is an error in the question or the choices provided.
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The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?a)10.0b)10.5c)11.0d)11.5Correct answer is option 'C'. Can you explain this answer?
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The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?a)10.0b)10.5c)11.0d)11.5Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?a)10.0b)10.5c)11.0d)11.5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?a)10.0b)10.5c)11.0d)11.5Correct answer is option 'C'. Can you explain this answer?.
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