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The mean and S.D. of 1,2,3,4,5,6 is
- a)3,3
- b)7/2,√3
- c)7/2,
- d)3, 35/12
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The mean and S.D. of 1,2,3,4,5,6 isa)3,3b)7/2,√3c)7/2,d)3, 35/12...
We are given the data: 1, 2, 3, 4, 5, 6
Step 1: Calculate the Mean
The formula for the mean is:
Mean = (Sum of all values) / (Number of values)
Substituting the values:
Mean = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 7/2
Step 2: Calculate the Variance
The formula for variance is:
Variance = Σ(xi - Mean)² / n
1. Subtract the mean (7/2) from each value and square the result:
- (1 - 7/2)² = (-5/2)² = 25/4
- (2 - 7/2)² = (-3/2)² = 9/4
- (3 - 7/2)² = (-1/2)² = 1/4
- (4 - 7/2)² = (1/2)² = 1/4
- (5 - 7/2)² = (3/2)² = 9/4
- (6 - 7/2)² = (5/2)² = 25/4
2. Sum the squared values:
(25/4) + (9/4) + (1/4) + (1/4) + (9/4) + (25/4) = 70/4 = 35/2
3. Divide by n (6):
Variance = (35/2) / 6 = 35/12
Step 3: Calculate the Standard Deviation
The standard deviation is the square root of the variance:
Standard Deviation = √(35/12)
Final Answer
The mean is 7/2, and the standard deviation is √(35/12).
Correct option: (c) 7/2, √(35/12)
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The mean and S.D. of 1,2,3,4,5,6 isa)3,3b)7/2,√3c)7/2,d)3, 35/12Correct answer is option 'C'. Can you explain this answer?
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