Sum of deviation of certain number of items measured from 2.5 is 50 an...
Given:
Sum of deviation from 2.5 = 50
Sum of deviation from 3.5 = -50
To Find:
Value of 'a' and 'x'
Solution:
Deviation means the difference between the observed value and the mean of the data set.
Let's consider a series of 'n' items:
x₁, x₂, x₃, ......., xn
We know that the sum of deviations from the mean is always equal to zero.
Σ(xi - mean) = 0
Mean = (Σxi)/n
We can rewrite the above equation as:
Σxi - n(mean) = 0
Σxi = n(mean)
Now, let's consider the deviation from 2.5.
Σ(xi - 2.5) = 50
We can rewrite this equation as:
Σxi - 2.5n = 50
Similarly, for deviation from 3.5,
Σ(xi - 3.5) = -50
We can rewrite this equation as:
Σxi - 3.5n = -50
Now, we have two equations and two variables (a and n).
We can solve these equations simultaneously to find the values of 'a' and 'n'.
Σxi - 2.5n = 50
Σxi - 3.5n = -50
Subtracting these equations, we get:
n = 100/1
n = 100
Substituting the value of 'n' in any one of the above equations, we get:
Σxi - 2.5n = 50
Σxi - 2.5(100) = 50
Σxi = 300
Now, we have the value of 'n' and the sum of the items(xi).
We can use these values to find the value of 'a'.
We know that:
x₁ + x₂ + x₃ + ...... + xn = Σxi
Substituting the value of Σxi, n and x₁ = a, we get:
a + (a + 1) + (a + 2) + ...... + (a + 99) = 300
Simplifying this equation, we get:
100a + 4950 = 300
100a = -4650
a = -46.5
Therefore, the value of 'a' is -46.5 and 'n' is 100.
Hence, the required values are:
a = -46.5
n = 100
Sum of deviation of certain number of items measured from 2.5 is 50 an...
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