If each entry of a piece of data is increased by 7, then the arithmetic mean:

Correct option is C

Given:

Let the original data be x₁ , x₂ , x₃ , . . . , x_n.

Formula Used:

Arithmetic mean = $$\frac{ (x₁ + x₂ + x₃ + . . . + x_n)}n$$​​

Solution:

If each entry is increased by 7, the new data becomes (x₁ + 7) , (x₂ + 7) , (x₃ + 7) , . . . , (xn + 7).

=> New arithmetic mean = $$\frac{[(x₁ + 7) + (x₂ + 7) + (x₃ + 7) + . . . + (xn + 7)]} n$$​​

=> New arithmetic mean = $$\frac{(x₁ + x₂ + x₃ + . . . + x_n)} n + \frac{(7 + 7 + 7 + . . . + 7)} n$$​​

=> New arithmetic mean = Arithmetic mean + 7

Thus, correct answer is option (c).