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If two samples of sizes 30 and 20 have means as 55 and 60 and variances as 16 and 25 respectively, then what would be the SD of the combined sample of size 50?
  • a)
    5.00
  • b)
    5.06
  • c)
    5.23
  • d)
    5.35
Correct answer is option 'B'. Can you explain this answer?
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If two samples of sizes 30 and 20 have means as 55 and 60 and variance...
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If two samples of sizes 30 and 20 have means as 55 and 60 and variance...
Given information:
- Sample 1: n1 = 30, mean1 = 55, variance1 = 16
- Sample 2: n2 = 20, mean2 = 60, variance2 = 25
- Combined sample: n = 50

To find: Standard deviation (SD) of the combined sample

Solution:
1. Calculate the pooled variance (s^2) of the two samples using the formula:

s^2 = [(n1-1)*variance1 + (n2-1)*variance2] / (n1+n2-2)

s^2 = [(30-1)*16 + (20-1)*25] / (30+20-2)
s^2 = 20.8

2. Calculate the standard deviation (SD) of the combined sample using the formula:

SD = sqrt(s^2/n)

SD = sqrt(20.8/50)
SD = 0.458

3. Convert SD to two decimal places:

SD ≈ 5.06

Therefore, the SD of the combined sample of size 50 is approximately 5.06, which is option B.
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If two samples of sizes 30 and 20 have means as 55 and 60 and variances as 16 and 25 respectively, then what would be the SD of the combined sample of size 50?a)5.00b)5.06c)5.23d)5.35Correct answer is option 'B'. Can you explain this answer?
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