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The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the standard deviations are 8 and 7. The mean and standard deviations of the combined sample is
  • a)
    m=50.57, σ=75.6
  • b)
    m=51.57, σ=7.35
  • c)
    m=515.7, σ=0.756
  • d)
    m=505.7, σ=7.56
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The means of two samples of sizes 50 and 100 respectively are 54.1 and...
Calculation of Mean and Standard Deviation of Combined Sample

Mean Calculation:
- The weighted average of the means of the two samples is calculated to find the mean of the combined sample.
- Mean of combined sample = (mean of sample 1 * size of sample 1 + mean of sample 2 * size of sample 2) / (size of sample 1 + size of sample 2)
- Mean of combined sample = (54.1 * 50 + 50.3 * 100) / (50 + 100) = (2705 + 5030) / 150 = 7735 / 150 = 51.57

Standard Deviation Calculation:
- The formula for combining standard deviations of two samples of different sizes is used.
- Standard deviation of combined sample = sqrt(((std deviation of sample 1)^2 * (size of sample 1 - 1) + (std deviation of sample 2)^2 * (size of sample 2 - 1)) / (size of sample 1 + size of sample 2 - 1))
- Standard deviation of combined sample = sqrt(((8^2 * 49) + (7^2 * 99)) / 149) = sqrt((64 * 49 + 49 * 99) / 149) = sqrt((3136 + 4851) / 149) = sqrt(7987 / 149) = sqrt(53.6) = 7.35
Therefore, the correct answer is option b) m=51.57, σ=7.35.
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The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the standard deviations are 8 and 7. The mean and standard deviations of the combined sample isa)m=50.57, σ=75.6b)m=51.57, σ=7.35c)m=515.7, σ=0.756d)m=505.7, σ=7.56Correct answer is option 'B'. Can you explain this answer?
Question Description
The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the standard deviations are 8 and 7. The mean and standard deviations of the combined sample isa)m=50.57, σ=75.6b)m=51.57, σ=7.35c)m=515.7, σ=0.756d)m=505.7, σ=7.56Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the standard deviations are 8 and 7. The mean and standard deviations of the combined sample isa)m=50.57, σ=75.6b)m=51.57, σ=7.35c)m=515.7, σ=0.756d)m=505.7, σ=7.56Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the standard deviations are 8 and 7. The mean and standard deviations of the combined sample isa)m=50.57, σ=75.6b)m=51.57, σ=7.35c)m=515.7, σ=0.756d)m=505.7, σ=7.56Correct answer is option 'B'. Can you explain this answer?.
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