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average marks of 20 students of a class was 48 a new student took admission with 52 marks whereas two existing student left the college if the marks of these students were 40 and 39 respectively find the average marks of the remaining student |
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Answer» Here,n 1 =10, X 1 =60 and σ 1 =4∴ ∑x i =60×10=600Now, n 2 =10, x 2 =40 and σ 2 =6∴ ∑x i =10×40=400⇒ Total marks of 20 students (∑x)=400+600=1000⇒ x = 201000 =50Now, σ 12 =(4) 2 ⇒ n 1 1 ∑ 110 x i2 −( x 1 ) 2 =16⇒ ∑ 110 x i2 =n 1 (16+( x 1 ) 2 ) =10(16+3600)⇒ ∑ 110 x i2 =36160Now, σ 2 =(6) 2 ⇒ n 2 1 ∑ 1120 x i2 −( x 2 ) 2 =36⇒ ∑ 1120 x i2 =(36+( x ) 2 )n 2 =(36+1600)10⇒ ∑ 1120 x i2 =16360Now, required standard deviation (σ)= n1 ∑x i2 − x 2 = 201 (36160+16360)−(50) 2 = 2626−2500 = 126 =11.5 |
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