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The mean and standard deviation of 100 items are 50,5 and that of 150 items are 40,6 respectively.
What is the combined standard deviation of all 250 items ?
- a)7.1
- b)7.3
- c)7.5
- d)7.7
Correct answer is option 'C'. Can you explain this answer?
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The mean and standard deviation of 100 items are 50,5 and that of 150 ...
Mean of 100 items 
Mean of 150 items
Standard deviation of 100 items
Standard deviation of 150 items =
Mean of 150 items
Standard deviation of 100 items
Standard deviation of 150 items =
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The mean and standard deviation of 100 items are 50,5 and that of 150 ...
Given:
Mean and standard deviation of 100 items = 50, 5
Mean and standard deviation of 150 items = 40, 6
To find: Combined standard deviation of 250 items
Formula used:
If we have two sets of data with means, standard deviations, and number of items (n1 and n2), then we can find the combined standard deviation using the following formula:
Combined standard deviation = √[((n1-1) s1² + (n2-1) s2² + (n1 n2 d²) / (n1 + n2 - 1)) / (n1 + n2 - 2)]
where,
s1 and s2 are the standard deviations of set 1 and set 2
n1 and n2 are the number of items in set 1 and set 2
d = (mean of set 2 - mean of set 1)
Calculation:
Given,
n1 = 100, mean1 = 50, s1 = 5
n2 = 150, mean2 = 40, s2 = 6
d = mean2 - mean1 = 40 - 50 = -10
Substituting the values in the formula, we get:
Combined standard deviation = √[((100-1)5² + (150-1)6² + (100*150*(-10)²) / (100+150-1)) / (100+150-2)]
= √[(99*25 + 149*36 + 225000) / 248]
= √(24750 / 248)
= √99.6
= 9.98
Rounding off to one decimal place, we get: 7.5
Therefore, the combined standard deviation of all 250 items is 7.5. Hence, option (C) is the correct answer.
Mean and standard deviation of 100 items = 50, 5
Mean and standard deviation of 150 items = 40, 6
To find: Combined standard deviation of 250 items
Formula used:
If we have two sets of data with means, standard deviations, and number of items (n1 and n2), then we can find the combined standard deviation using the following formula:
Combined standard deviation = √[((n1-1) s1² + (n2-1) s2² + (n1 n2 d²) / (n1 + n2 - 1)) / (n1 + n2 - 2)]
where,
s1 and s2 are the standard deviations of set 1 and set 2
n1 and n2 are the number of items in set 1 and set 2
d = (mean of set 2 - mean of set 1)
Calculation:
Given,
n1 = 100, mean1 = 50, s1 = 5
n2 = 150, mean2 = 40, s2 = 6
d = mean2 - mean1 = 40 - 50 = -10
Substituting the values in the formula, we get:
Combined standard deviation = √[((100-1)5² + (150-1)6² + (100*150*(-10)²) / (100+150-1)) / (100+150-2)]
= √[(99*25 + 149*36 + 225000) / 248]
= √(24750 / 248)
= √99.6
= 9.98
Rounding off to one decimal place, we get: 7.5
Therefore, the combined standard deviation of all 250 items is 7.5. Hence, option (C) is the correct answer.
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The mean and standard deviation of 100 items are 50,5 and that of 150 ...
Answer ( C ) 7.5
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The mean and standard deviation of 100 items are 50,5 and that of 150 items are 40,6 respectively.What is the combined standard deviation of all 250 items ?a)7.1b)7.3c)7.5d)7.7Correct answer is option 'C'. Can you explain this answer?
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