The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. One rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases. (i) If wrong item is omitted(ii) If it is replaced by 12.

Question

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. One rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases. (i)      If wrong item is omitted(ii)     If it is replaced by 12.

Filo · Accepted Answer

Solution: x=n∑xi​​=10=20∑xi​​ ∑xi​=200 for 19 terms =200−8=192=∑xi​ σ=n1​⋅∑xi2​−(x)2​ let incorrect sum be e∑2=n1​⋅e∑xi2​−100​ 4=201​e∑xi2​−100 e∑xi2​=104⋅20=2080 correct ∑xi2​ for 19 terms = 2080−64=2016 (i)x=19192​=10.1 σ=191​⋅2016−(10.1)2​ =106.1−102​=4.1​=2.024 (ii) n = 20 ∑xi​=204 ∑xi2​=2016+144=2160 x=20204​=10.2 σ=201​⋅2160−(10.2)2​ =108−104.04​=3.96​=1.98

Question Text	The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. One rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases. (i) If wrong item is omitted(ii) If it is replaced by 12.
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The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. One rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases. (i) If wrong item is omitted(ii) If it is replaced by 12.

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