In an experiment with 15 observations on x, the following results were available Sigma x2=2830, Sigma x=170 One observation that was 20, was found to be wrong and was replaced by the correct value 30. Then the corrected variance is :

Question

In an experiment with 15 observations on x, the following results were available Sigma x2=2830, Sigma x=170 One observation that was 20, was found to be wrong and was replaced by the correct value 30. Then the corrected variance is : (A) 78.00 (B) 188.66 (C) 177.33 (D) 8.33

Tardigrade Admin · Accepted Answer

Given N=15 Sigma x2=2830, Sigma x=170 One observation 20 was replaced by 30, then Sigma x2 = 2830 - 400 + 900 = 3330 Sigma x = 170 - 20 + 30 = 180 Varience, σ2 = ( Sigma x2/N) - (( Sigma x/N))2 = (3330/15) - ((180/15))2 = (3330 - 15 × 144/15) = (3330 - 2160/15) = (1170/15) = 78.0

Q. In an experiment with 15 observations on x, the following results were available Σx2=2830,Σx=170 One observation that was 20, was found to be wrong and was replaced by the correct value 30. Then the corrected variance is :

78.00

188.66

177.33

8.33

Given N=15 Σx2=2830,Σx=170 One observation 20 was replaced by 30, then Σx2=2830−400+900=3330 Σx=170−20+30=180 Varience, σ2=NΣx2​−(NΣx​)2 =153330​−(15180​)2 =153330−15×144​ =153330−2160​=151170​=78.0

Q. In an experiment with $15$ observations on $x$ , the following results were available $Σ x^{2} = 2830, Σ x = 170$ One observation that was $20$ , was found to be wrong and was replaced by the correct value $30$ . Then the corrected variance is :