Question

If 10 is added to every observation of data, then the new arithmetic mean will

Answer 1

Answer:

x+10

represent the observation gotten with x. so its going to be x+10

Answer 2

Answer:

The new mean is the original mean + 10

Step-by-step explanation:

Let the observations be = x₁ , x₂ , . . . . . . , xₙ i.e. n observations.

Let the original mean be m₁

Therefore, m₁ = $\frac{x_1+x_2 + . . . +x_n}{n}$

Now 10 is added to each observation,

Therefore, the observations become = x₁ + 10 , x₂ + 10 , . . . . . . , xₙ + 10

Let the new mean be m₂

Therefore, m₂ = $\frac{(x_1+10)+(x_2+10) + . . . +(x_n+10)}{n}$

                        = $\frac{x_1+x_2 + . . . +x_n + 10n}{n}$

                        = $\frac{x_1+x_2 + . . . +x_n}{n}$ + $\frac{10n}{n}$

                        = $\frac{x_1+x_2 + . . . +x_n}{n}$ + 10

                        = m₁ + 10

Therefore, the new mean is the original mean + 10