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the mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. find the mean and standard deviation if the incorrect observations are omitted.

the mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. find the mean and standard deviation if the incorrect observations are omitted.

Grade:Upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
Hello student,
Incorrect eman = 20 and incorrect S.D. =3.
Hence, \sum_{i=1}^{n}\frac{x_{i}}{100}= 20
This gives Σ xi = 2000
corrected Σ xi = 2000-21-21-18 = 1940
correct mean = 1940/97 = 20.
Incorrect S.D. = 3
Incorrect variance = 9.
\frac{1}{100}(incorrect \sum_{i=1}^{n}x_{i}^{2}) - (incorrect mean)^{2} = 9
\frac{1}{100}(incorrect \sum_{i=1}^{n}x_{i}^{2}) - 400= 9
incorrect \sum_{i=1}^{n}x_{i}^{2} = 40900
Correct Σxi2 = 40900 – 212 - 212 - 182
Correct Σxi2 = 39694
Hence, variance of remaining observations = 39694/ 97 – (20)2
= 409.216 – 400
= 9.216
Hence, corrected S.D. = √9.216 = 3.035

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