For a statistical data x ₁, x ₂, , x ₁₀ of 10 values, a student obtained the mean as 5.5 and _ i=1 ¹⁰ x_i^2=371 . He later found that he had noted two values in the data incorrectly as 4 and 5 , instead of the correct values 6 and 8 , respe

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For a statistical data x ₁, x ₂, , x ₁₀ of 10 values, a student obtained the mean as 5.5 and _ i=1 ¹⁰ x_i^2=371 . He later found that he had noted two values in the data incorrectly as 4 and 5 , instead of the correct values 6 and 8 , respectively. The variance of the corrected data is

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Correct answer: C. 7

aligned & Mean x =5.5 & = _ i =1 ¹⁰ x _ i =5.5 10=55 & = _ i =1 ¹⁰ x _ i ^2=371 & ( x _ i )_ new =55-(4+5)+(6+8)=60 & & ( x _ i ^2 )_ new =371- (4^2+5^2 )+ (6^2+8^2 )=430 aligned aligned & Variance ^2= x _ i ^2 10 - ( x _ i 10 )^2 & ^2= 430 10 - ( 60 10 )^2 & ^2=43-36 & ^2=7 aligned

For a statistical data x ₁, x ₂, , x ₁₀ of 10 values, a student obtained the mean as 5.5 and _ i=1 ¹⁰ x_i^2=371 . He later found that he had noted two values in the data incorrectly as 4 and 5 , instead of the correct values 6 and 8 , respectively. The variance of the corrected data is

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