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The mean and sd for a group of 100 observation are 65 and 7.03 .If 60 observation have mean and sd as 70 and 3 ,what is the sd for group comprising 40 observation?
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The mean and sd for a group of 100 observation are 65 and 7.03 .If 60 ...
Given:
To find: SD for a group comprising 40 observations
Solution:
Step 1: Find the new mean
Step 2: Find the new variance
Step 3: Find the new SD
Therefore, the SD for a group comprising 40 observations is 17.76.
- Mean = 65
- SD = 7.03
- 60 observations have mean = 70 and SD = 3
To find: SD for a group comprising 40 observations
Solution:
Step 1: Find the new mean
- Total number of observations = 100
- Number of observations with mean = 70 and SD = 3 = 60
- Number of observations with mean = 65 and SD = 7.03 = 100 - 60 = 40
- New mean = (60 * 70 + 40 * 65) / 100 = 67
Step 2: Find the new variance
- Var(X) = [n1 * (SD1)^2 + n2 * (SD2)^2 + n1 * (mean1)^2 + n2 * (mean2)^2 - n * (mean)^2] / n
- Substituting the given values, we get Var(X) = [60 * (3)^2 + 40 * (7.03)^2 + 60 * (70)^2 + 40 * (65)^2 - 100 * (67)^2] / 100 = 315.09
Step 3: Find the new SD
- SD(X) = sqrt(Var(X)) = sqrt(315.09) = 17.76
Therefore, the SD for a group comprising 40 observations is 17.76.
Community Answer
The mean and sd for a group of 100 observation are 65 and 7.03 .If 60 ...
The variance of data 3,4,5,8 is
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The mean and sd for a group of 100 observation are 65 and 7.03 .If 60 observation have mean and sd as 70 and 3 ,what is the sd for group comprising 40 observation?
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The mean and sd for a group of 100 observation are 65 and 7.03 .If 60 observation have mean and sd as 70 and 3 ,what is the sd for group comprising 40 observation? 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 observation are 65 and 7.03 .If 60 observation have mean and sd as 70 and 3 ,what is the sd for group comprising 40 observation? 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 observation are 65 and 7.03 .If 60 observation have mean and sd as 70 and 3 ,what is the sd for group comprising 40 observation?.
The mean and sd for a group of 100 observation are 65 and 7.03 .If 60 observation have mean and sd as 70 and 3 ,what is the sd for group comprising 40 observation? 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 observation are 65 and 7.03 .If 60 observation have mean and sd as 70 and 3 ,what is the sd for group comprising 40 observation? 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 observation are 65 and 7.03 .If 60 observation have mean and sd as 70 and 3 ,what is the sd for group comprising 40 observation?.
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