If X̅ is the mean of x1, x2, x3, ...xn, then for a ≠ 0, the mean of (ax1, ax2, ax3, ... axn is:

Answer (Detailed Solution Below)

Option 1 :

Detailed Solution

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Given:

The mean of x1, x2, x3, ... xn is X̅.

We need to find the mean of the transformed values:

(ax1, ax2, ax3, ..., axn) and (x1/a, x2/a, x3/a, ..., xn/a).

Formula used:

The mean of a set of values {x1, x2, ..., xn} is:

X̅ = (x1 + x2 + ... + xn) / n

For a transformation involving multiplication by a constant **a** and division by **a**:

Calculation:

Mean of {ax1, ax2, ..., axn}:

⇒ (ax1 + ax2 + ... + axn) / n

⇒ a (x1 + x2 + ... + xn) / n

⇒ aX̅

Mean of {x1/a, x2/a, ..., xn/a}:

⇒ (x1/a + x2/a + ... + xn/a) / n

⇒ (1/a) (x1 + x2 + ... + xn) / n

⇒ (1/a) X̅

∴ The mean of the given transformed values is (a + 1/a).

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