The mean of 5 observations Is 10. If each observation of the data is increased by 5. Find the new man
Answers
Answer:
New mean is 15.
Step-by-step 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.
Answer:
New mean is 15.
Step-by-step 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.