The mean of 5 observations is 10 9 of each observabon of the data in increrased by 5 find new mean​

Question

The mean of 5 observations is 10 9 of each observabon of the data in increrased by 5 find new mean​

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Natalia 1 month 2021-08-17T19:45:41+00:00 1 Answer 0 views 0

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    2021-08-17T19:47:19+00:00

    Answer:


    New mean is 15.



    Explanation:


    Let the five observations are x₁ , x₂ , x₃ , x₄ , x₅.


    According to the question,


    Mean = 10


    Number of observations = 5


    Sum of observations = x₁ + x₂ + x₃ + x₄ + x₅



    We know ( formula ),


    Mean = ( sum of observations ) / number of observations



    Hence,


    = >  10 = ( x₁ + x₂ + x₃ + x₄ + x₅ ) / 5


    = >  50 = x₁ + x₂ + x₃ + x₄ + x₅   …( i )


    When each observation of the data is increased by 5 : –


    Sum of observations = x₁ + 5 + x₂ + 5 + x₃ + 5 + x₄ + 5 + x₅ + 5



    = >  Mean = ( x₁ + 5 + x₂ + 5 + x₃ + 5 + x₄ + 5 + x₅ + 5 ) / 5


    = >  Mean = ( x₁ + x₂ + x₃ + x₄ + x₅ + 5 + 5 + 5 + 5 + 5 ) / 5  



    From ( i ) , substituting the value of x₁ + x₂ + x₃ + x₄ + x₅,


    = >  Mean = ( 50 + 25 ) / 5


    = >  Mean = 75 / 5


    = >  Mean = 15


    Therefore the new mean is 15.

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