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The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is
- a)3.98
- b)4.02
- c)3.99
- d)4.01
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The mean and variance of 20 observations are found to be 10 and 4, res...
Now, actual mean
=
∴ Actual variance =
106 - (10.1)2 = 106 - 102.01
= 3.99
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Community Answer
The mean and variance of 20 observations are found to be 10 and 4, res...
Given:
- Mean of 20 observations = 10
- Variance of 20 observations = 4
To find:
- Correct variance after correcting the observation
Solution:
Step 1: Calculate the sum of all observations:
- Mean = Sum of all observations / Number of observations
- Sum of all observations = Mean * Number of observations
- Sum of all observations = 10 * 20
- Sum of all observations = 200
Step 2: Calculate the sum of squares of all observations:
- Variance = (Sum of squares of all observations - (Sum of all observations)^2 / Number of observations) / Number of observations
- Variance = (Sum of squares of all observations - (200)^2 / 20) / 20
- Variance = (Sum of squares of all observations - 40000 / 20) / 20
- Variance = (Sum of squares of all observations - 2000) / 20
Step 3: Calculate the sum of squares of incorrect observation:
- Sum of squares of incorrect observation = (9)^2
- Sum of squares of incorrect observation = 81
Step 4: Calculate the sum of squares of correct observation:
- Sum of squares of correct observation = (11)^2
- Sum of squares of correct observation = 121
Step 5: Calculate the sum of squares of all observations after correction:
- Sum of squares of all observations after correction = (Sum of squares of all observations - Sum of squares of incorrect observation) + Sum of squares of correct observation
- Sum of squares of all observations after correction = (Sum of squares of all observations - 81) + 121
- Sum of squares of all observations after correction = Sum of squares of all observations + 40
Step 6: Calculate the corrected variance:
- Corrected variance = (Sum of squares of all observations after correction - 40000 / 20) / 20
- Corrected variance = (Sum of squares of all observations + 40 - 2000) / 20
- Corrected variance = (Sum of squares of all observations - 1960) / 20
Step 7: Substitute the given values:
- Corrected variance = (4 - 1960) / 20
- Corrected variance = -1956 / 20
- Corrected variance = -97.8
Conclusion:
The correct variance after correcting the observation is -97.8. However, variances cannot be negative. Therefore, there must be an error in the given options.
- Mean of 20 observations = 10
- Variance of 20 observations = 4
To find:
- Correct variance after correcting the observation
Solution:
Step 1: Calculate the sum of all observations:
- Mean = Sum of all observations / Number of observations
- Sum of all observations = Mean * Number of observations
- Sum of all observations = 10 * 20
- Sum of all observations = 200
Step 2: Calculate the sum of squares of all observations:
- Variance = (Sum of squares of all observations - (Sum of all observations)^2 / Number of observations) / Number of observations
- Variance = (Sum of squares of all observations - (200)^2 / 20) / 20
- Variance = (Sum of squares of all observations - 40000 / 20) / 20
- Variance = (Sum of squares of all observations - 2000) / 20
Step 3: Calculate the sum of squares of incorrect observation:
- Sum of squares of incorrect observation = (9)^2
- Sum of squares of incorrect observation = 81
Step 4: Calculate the sum of squares of correct observation:
- Sum of squares of correct observation = (11)^2
- Sum of squares of correct observation = 121
Step 5: Calculate the sum of squares of all observations after correction:
- Sum of squares of all observations after correction = (Sum of squares of all observations - Sum of squares of incorrect observation) + Sum of squares of correct observation
- Sum of squares of all observations after correction = (Sum of squares of all observations - 81) + 121
- Sum of squares of all observations after correction = Sum of squares of all observations + 40
Step 6: Calculate the corrected variance:
- Corrected variance = (Sum of squares of all observations after correction - 40000 / 20) / 20
- Corrected variance = (Sum of squares of all observations + 40 - 2000) / 20
- Corrected variance = (Sum of squares of all observations - 1960) / 20
Step 7: Substitute the given values:
- Corrected variance = (4 - 1960) / 20
- Corrected variance = -1956 / 20
- Corrected variance = -97.8
Conclusion:
The correct variance after correcting the observation is -97.8. However, variances cannot be negative. Therefore, there must be an error in the given options.
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The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance isa)3.98b)4.02c)3.99d)4.01Correct answer is option 'C'. Can you explain this answer?
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