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 incorrect observations are omitted.

Question

Arun · Answer

Dear Yashika

Hello student,
Incorrect eman = 20 and incorrect S.D. =3.
Hence, $\sum_{i=1}^{n}\frac{x_{i}}{100}= 20$
This gives S x_i = 2000
corrected S x_i= 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 Sx_i² = 40900 – 21²- 21²- 18²
Correct Sx_i² = 39694
Hence, variance of remaining observations = 39694/ 97 – (20)²
= 409.216 – 400
= 9.216
Hence, corrected S.D. = v9.216 = 3.035

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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 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 incorrect observations are omitted.

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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 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 incorrect observations are omitted.

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