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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 mean of all 250 items ?
- a)43
- b)44
- c)45
- d)46
Correct answer is option 'B'. 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 Information:
- Mean of 100 items = 50
- Standard deviation of 100 items = 5
- Mean of 150 items = 40
- Standard deviation of 150 items = 6
To Find:
- Combined mean of all 250 items
Approach:
To find the combined mean of all 250 items, we need to consider the weights of each group of items. The weights are given by the number of items in each group.
Solution:
1. Calculate the total sum of all 250 items:
- Sum of 100 items = 100 * 50 = 5000
- Sum of 150 items = 150 * 40 = 6000
- Total sum of all 250 items = 5000 + 6000 = 11000
2. Calculate the total weight of all 250 items:
- Total weight = 100 + 150 = 250
3. Calculate the weighted mean:
- Weighted mean = (Sum of all items) / (Total weight)
- Weighted mean = 11000 / 250 = 44
Answer:
The combined mean of all 250 items is 44 (Option B).
- Mean of 100 items = 50
- Standard deviation of 100 items = 5
- Mean of 150 items = 40
- Standard deviation of 150 items = 6
To Find:
- Combined mean of all 250 items
Approach:
To find the combined mean of all 250 items, we need to consider the weights of each group of items. The weights are given by the number of items in each group.
Solution:
1. Calculate the total sum of all 250 items:
- Sum of 100 items = 100 * 50 = 5000
- Sum of 150 items = 150 * 40 = 6000
- Total sum of all 250 items = 5000 + 6000 = 11000
2. Calculate the total weight of all 250 items:
- Total weight = 100 + 150 = 250
3. Calculate the weighted mean:
- Weighted mean = (Sum of all items) / (Total weight)
- Weighted mean = 11000 / 250 = 44
Answer:
The combined mean of all 250 items is 44 (Option B).
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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 mean of all 250 items ?a)43b)44c)45d)46Correct answer is option 'B'. Can you explain this answer?
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