If the sum of the deviations of a set of values x1,x2,x3,......xn measured from 50 is (-10) and the sum of deviations of the values from 46 is 70 ,then find its mean.
Answers
As we know the sets of values as x₁, x₂, x₃ ,..., xₙ.
‡‡The sum of the deviations of a set of values measured from 50 is –10.
→ (x₁ - 50) + (x₂-50) + (x₃-50) + ... + (xₙ-50) = –10
→ (x₁ + x₂ + x₃ + ... + xₙ) –50n = –10
→ (x₁ + x₂ + x₃ + ... + xₙ) = 50n –10 ...[1]
‡‡The sum of the deviations of a set of values measured from 46 is 70.
→ (x₁ - 46) + (x₂-46) + (x₃-46) + ... + (xₙ-46) = 70
→ (x₁ + x₂ + x₃ + ... + xₙ) –46n = 70
→ (x₁ + x₂ + x₃ + ... + xₙ) = 46n + 70 ...[2]
________
Putting Both the EQUATIONS.
→ 50n –10 = 46n + 70
→ 50n–46n = 70+10
→ 4n = 80
→ n = 20
★Putting values of n into any ONE OF THE EQUATION to find the SUM OF DEVIATION.
→ 46n+70
→46(20)+70
→920+70
→ 990
Finally, We can find the MEAN of the datas we have.
- → 990/n = 990/20 = 49.5