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The mean and SD for a group of 100 observations are 65 and 7.03 respectively. If 60 of these observations have mean and SD as 70 and 3 respectively, what is the SD for the group comprising 40 observations?
- a)16
- b)25
- c)4
- d)2
Correct answer is option 'C'. Can you explain this answer?
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The mean and SD for a group of 100 observations are 65 and 7.03 respec...
Given information:
- Mean of 100 observations = 65
- Standard deviation of 100 observations = 7.03
- Mean of 60 observations = 70
- Standard deviation of 60 observations = 3
- We need to find the standard deviation of the remaining 40 observations.
Formula to calculate the combined standard deviation :
SD1 = Standard deviation of first set of observations
SD2 = Standard deviation of second set of observations
n1 = Number of observations in first set
n2 = Number of observations in second set
SD = Standard deviation of the combined set of observations
SD = √[(n1-1)SD1^2 + (n2-1)SD2^2 / (n1+n2-2)]
Calculating the combined standard deviation of the 60 observations:
SD1 = 3
n1 = 60
SD2 = 7.03
n2 = 40
SD60 = √[(60-1)3^2 + (40-1)7.03^2 / (60+40-2)]
SD60 = √[1772.39 / 98]
SD60 = √18.08
SD60 = 4.25
Therefore, the standard deviation of the remaining 40 observations is 4.25, which is closest to option C (4).
- Mean of 100 observations = 65
- Standard deviation of 100 observations = 7.03
- Mean of 60 observations = 70
- Standard deviation of 60 observations = 3
- We need to find the standard deviation of the remaining 40 observations.
Formula to calculate the combined standard deviation :
SD1 = Standard deviation of first set of observations
SD2 = Standard deviation of second set of observations
n1 = Number of observations in first set
n2 = Number of observations in second set
SD = Standard deviation of the combined set of observations
SD = √[(n1-1)SD1^2 + (n2-1)SD2^2 / (n1+n2-2)]
Calculating the combined standard deviation of the 60 observations:
SD1 = 3
n1 = 60
SD2 = 7.03
n2 = 40
SD60 = √[(60-1)3^2 + (40-1)7.03^2 / (60+40-2)]
SD60 = √[1772.39 / 98]
SD60 = √18.08
SD60 = 4.25
Therefore, the standard deviation of the remaining 40 observations is 4.25, which is closest to option C (4).
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The mean and SD for a group of 100 observations are 65 and 7.03 respectively. If 60 of these observations have mean and SD as 70 and 3 respectively, what is the SD for the group comprising 40 observations?a)16b)25c)4d)2Correct answer is option 'C'. Can you explain this answer?
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The mean and SD for a group of 100 observations are 65 and 7.03 respectively. If 60 of these observations have mean and SD as 70 and 3 respectively, what is the SD for the group comprising 40 observations?a)16b)25c)4d)2Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The mean and SD for a group of 100 observations are 65 and 7.03 respectively. If 60 of these observations have mean and SD as 70 and 3 respectively, what is the SD for the group comprising 40 observations?a)16b)25c)4d)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean and SD for a group of 100 observations are 65 and 7.03 respectively. If 60 of these observations have mean and SD as 70 and 3 respectively, what is the SD for the group comprising 40 observations?a)16b)25c)4d)2Correct answer is option 'C'. Can you explain this answer?.
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