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 if wrong item is omitted
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Step-by-step explanation:
(i) Given, number of observations n=20
Incorrect mean =10
Incorrect standard deviation =2
xˉ=n1i=1∑20xi
10=201i=1∑20xi
⇒i=1∑20xi=200
So, the incorrect sum of observations =200
Correct sum of observation =200−8=192
⇒ Correct mean =19Correctsum=19192=10.1
Standard deviation σ=n1i=1∑nxi2−n21(i=1∑nxi)2=n1
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