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

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