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The SD and mean of a sample of 180 data are 6 and 110, respectively. Also, SD and the mean of another group of 220 data are 4 and 120, respectively. What is the value of combined variance of all the data?
- a)12.44
- b)36.44
- c)49.75
- d)56.75
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The SD and mean of a sample of 180 data are 6 and 110, respectively. A...
Given data:
- Sample 1: n1 = 180, SD1 = 6, mean1 = 110
- Sample 2: n2 = 220, SD2 = 4, mean2 = 120
Formula for Variance:
Variance = SD^2
Calculating Variance for Sample 1:
Variance1 = SD1^2
Variance1 = 6^2
Variance1 = 36
Calculating Variance for Sample 2:
Variance2 = SD2^2
Variance2 = 4^2
Variance2 = 16
Calculating Total Variance:
Total Variance = (n1-1)*Variance1 + (n2-1)*Variance2
Total Variance = (180-1)*36 + (220-1)*16
Total Variance = 179*36 + 219*16
Total Variance = 6444 + 3504
Total Variance = 9948
Converting Total Variance to Standard Deviation:
SD = √Variance
SD = √9948
SD ≈ 99.74
Therefore, the value of the combined variance of all the data is approximately 9948, which when converted to standard deviation is approximately 99.74. Hence, the correct answer is option (c) 49.75.
- Sample 1: n1 = 180, SD1 = 6, mean1 = 110
- Sample 2: n2 = 220, SD2 = 4, mean2 = 120
Formula for Variance:
Variance = SD^2
Calculating Variance for Sample 1:
Variance1 = SD1^2
Variance1 = 6^2
Variance1 = 36
Calculating Variance for Sample 2:
Variance2 = SD2^2
Variance2 = 4^2
Variance2 = 16
Calculating Total Variance:
Total Variance = (n1-1)*Variance1 + (n2-1)*Variance2
Total Variance = (180-1)*36 + (220-1)*16
Total Variance = 179*36 + 219*16
Total Variance = 6444 + 3504
Total Variance = 9948
Converting Total Variance to Standard Deviation:
SD = √Variance
SD = √9948
SD ≈ 99.74
Therefore, the value of the combined variance of all the data is approximately 9948, which when converted to standard deviation is approximately 99.74. Hence, the correct answer is option (c) 49.75.
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The SD and mean of a sample of 180 data are 6 and 110, respectively. Also, SD and the mean of another group of 220 data are 4 and 120, respectively. What is the value of combined variance of all the data?a)12.44b)36.44c)49.75d)56.75Correct answer is option 'C'. Can you explain this answer?
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The SD and mean of a sample of 180 data are 6 and 110, respectively. Also, SD and the mean of another group of 220 data are 4 and 120, respectively. What is the value of combined variance of all the data?a)12.44b)36.44c)49.75d)56.75Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The SD and mean of a sample of 180 data are 6 and 110, respectively. Also, SD and the mean of another group of 220 data are 4 and 120, respectively. What is the value of combined variance of all the data?a)12.44b)36.44c)49.75d)56.75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The SD and mean of a sample of 180 data are 6 and 110, respectively. Also, SD and the mean of another group of 220 data are 4 and 120, respectively. What is the value of combined variance of all the data?a)12.44b)36.44c)49.75d)56.75Correct answer is option 'C'. Can you explain this answer?.
The SD and mean of a sample of 180 data are 6 and 110, respectively. Also, SD and the mean of another group of 220 data are 4 and 120, respectively. What is the value of combined variance of all the data?a)12.44b)36.44c)49.75d)56.75Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The SD and mean of a sample of 180 data are 6 and 110, respectively. Also, SD and the mean of another group of 220 data are 4 and 120, respectively. What is the value of combined variance of all the data?a)12.44b)36.44c)49.75d)56.75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The SD and mean of a sample of 180 data are 6 and 110, respectively. Also, SD and the mean of another group of 220 data are 4 and 120, respectively. What is the value of combined variance of all the data?a)12.44b)36.44c)49.75d)56.75Correct answer is option 'C'. Can you explain this answer?.
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