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.

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Solution

Number of observations (n) = 100

Incorrect mean

Incorrect standard deviation

∴ Incorrect sum of observations = 2000

⇒ Correct sum of observations = 2000 – 21 – 21 – 18 = 2000 – 60 = 1940

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Similar questions

The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation when

(i) the wrong item is omitted,

(ii) the wrong item is replaced by 12.

Q. Mean and standard deviation of

20

observations are found to be

10

and

2

respectively , On rechecking it was found that an observation

8

was incorrect. Calculate the correct mean and standard deviation if

8

is replaced by

12

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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.

Number of observations (n) = 100 Incorrect mean Incorrect standard deviation ∴ Incorrect sum of observations = 2000 ⇒ Correct sum of observations = 2000 – 21 – 21 – 18 = 2000 – 60 = 1940

Number of observations (n) = 100

Incorrect mean

Incorrect standard deviation

∴ Incorrect sum of observations = 2000

⇒ Correct sum of observations = 2000 – 21 – 21 – 18 = 2000 – 60 = 1940