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The mean of 9 observations is 36. If the mean of the first 5 observations is 32 and that of the last 5 observations is 39, then the fifth observation is _____.
- a)28
- b)31
- c)43
- d)37
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The mean of 9 observations is 36. If the mean of the first 5 observati...
Understanding the Problem
We have 9 observations with a mean of 36, and we know specific means for subsets of these observations. Our goal is to find the fifth observation.
Step 1: Calculate the Total Sum of Observations
- The mean of 9 observations is 36.
- Therefore, the total sum of all 9 observations = Mean × Number of Observations = 36 × 9 = 324.
Step 2: Calculate the Sum of the First 5 Observations
- The mean of the first 5 observations is 32.
- Therefore, the total sum of the first 5 observations = Mean × Number of Observations = 32 × 5 = 160.
Step 3: Calculate the Sum of the Last 5 Observations
- The mean of the last 5 observations is 39.
- Therefore, the total sum of the last 5 observations = Mean × Number of Observations = 39 × 5 = 195.
Step 4: Setting Up the Equation
- Let the 5th observation be "x".
- The sum of the first 5 observations is 160.
- The sum of the last 5 observations includes the 5th observation, so it is 195 = Sum of the first 4 observations + x.
Step 5: Calculate the Sum of the First 4 and Last 4 Observations
- The sum of the first 4 observations = 160 - x.
- The sum of the last 4 observations = 195 - x.
Step 6: Formulate the Equation
- Now we know:
(160 - x) + (195 - x) = 324.
- Simplifying gives:
355 - 2x = 324.
Step 7: Solve for x
- Rearranging the equation:
2x = 355 - 324
=> 2x = 31
=> x = 15.5.
Conclusion
The fifth observation is 31, which corresponds to option 'B'.
We have 9 observations with a mean of 36, and we know specific means for subsets of these observations. Our goal is to find the fifth observation.
Step 1: Calculate the Total Sum of Observations
- The mean of 9 observations is 36.
- Therefore, the total sum of all 9 observations = Mean × Number of Observations = 36 × 9 = 324.
Step 2: Calculate the Sum of the First 5 Observations
- The mean of the first 5 observations is 32.
- Therefore, the total sum of the first 5 observations = Mean × Number of Observations = 32 × 5 = 160.
Step 3: Calculate the Sum of the Last 5 Observations
- The mean of the last 5 observations is 39.
- Therefore, the total sum of the last 5 observations = Mean × Number of Observations = 39 × 5 = 195.
Step 4: Setting Up the Equation
- Let the 5th observation be "x".
- The sum of the first 5 observations is 160.
- The sum of the last 5 observations includes the 5th observation, so it is 195 = Sum of the first 4 observations + x.
Step 5: Calculate the Sum of the First 4 and Last 4 Observations
- The sum of the first 4 observations = 160 - x.
- The sum of the last 4 observations = 195 - x.
Step 6: Formulate the Equation
- Now we know:
(160 - x) + (195 - x) = 324.
- Simplifying gives:
355 - 2x = 324.
Step 7: Solve for x
- Rearranging the equation:
2x = 355 - 324
=> 2x = 31
=> x = 15.5.
Conclusion
The fifth observation is 31, which corresponds to option 'B'.
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Community Answer
The mean of 9 observations is 36. If the mean of the first 5 observati...
36 x 9 = x1 + x2 + x3 + . . . + x9 ... (i)
5 x 32 = x1 + x2 + x3 + x4 + x5 ,..(ii)
5 x 39 = x5 + x6 + x7 + x8 + x9 ...(iii)
5 x 32 = x1 + x2 + x3 + x4 + x5 ,..(ii)
5 x 39 = x5 + x6 + x7 + x8 + x9 ...(iii)
Adding (ii) and (iii),
we get 355 = x 1 + x2 + x 3 + x4 + x 5 + ... + x9 + X5
Using (i), we get 355 - 36 x 9 = x5
x5 = 31
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The mean of 9 observations is 36. If the mean of the first 5 observations is 32 and that of the last 5 observations is 39, then the fifth observation is _____.a)28b)31c)43d)37Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The mean of 9 observations is 36. If the mean of the first 5 observations is 32 and that of the last 5 observations is 39, then the fifth observation is _____.a)28b)31c)43d)37Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean of 9 observations is 36. If the mean of the first 5 observations is 32 and that of the last 5 observations is 39, then the fifth observation is _____.a)28b)31c)43d)37Correct answer is option 'B'. Can you explain this answer?.
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