Question

.If a constant value is added to every observation of data, then arithmetic mean is obtained by:
(A) Subtracting the constant
(B) Adding the constant
(C) Multiplying the constant
m) Dividing the constant​

Answer 1

Answer:

c. mul multiplying the constant

Answer 2

Answer:

The correct answer is Option(B)

Explanation:

Recall the formula,

Arithmetic mean  of 'n' observations $a_1,a_2,a_3,a_4, ...........,a_n$

is given by, A = $\frac{a_1 + a_2 + a_3 + a_4 + ........... +a_n}{n}$

If a constant value 'x' is added to all the observations,

then the new Arithmetic mean   = $\frac{a_1+x + a_2 +x + .....................+a_n +x}{n}$

= $\frac{a_1 + a_2 + .....................+a_n +nx}{n}$$\frac{a_1 + a_2 + .....................+a_n}{n} + \frac{nx}{n}$

= A + x

Hence,

If a constant value is added to every observation of data, then the new arithmetic mean is obtained by adding the constant

The correct answer is Option(B)