the mean and standard deviation of 100 observations were calculated as 40 and 5.1 resp. by a student who took by mistake 50 instead of 40 for one observation. what are correct mean and standard deviation?

Given, x¯= 40 , σ= 5.1
According to the formula
x¯=xxnSo,xx = nx¯ =100×40=4000 Now This sum is incorrect, So for correct sum we will subtract old vlaue and add new value So, New (Correct)sum=4000-50+40=4000-10=3990 So, Now means i.e. correct x¯ =3990100=39.9 Now given σ=5.1 According to formula σ2=xx2n-x¯2 5.12=xx2100-402 xx2100=5.12+402 =1626.01 So, xx2 =1626.01×100=162601 But calculated xx2 is incorrect, so for correct sum of square we subtract square of 50 and ass square of 40 So, new xx2=162601-502+402=161701 So, correct σ2=correct xx2n-correct x¯2 correct σ2 =161701100-39.92=1617.01-1592.01=25 So, σ =25=5 Hence new mean is 39.9 and standard deviation is 5

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refer to NCERT t.b example...

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