Answer:
Step-by-step explanation:
Suppose there is the addition of a constant "b" to each generic dataset, then, new mean = old mean + b. This will affect the variance and the standard deviation of the resulting dataset to remain the same:
From the information given:
[tex]\mathbf{x_1,x_2,x_3...x_n \ have \ mean \ \overline x }[/tex]
Proof:
If c is added to each data set:
Then,
[tex]\mathbf{x_1+c,x_2+c,x_3+c...x_n+c \ and \ the \ new \ mean \ \overline x = \overline x + c}[/tex]
also;
[tex]\mathbf{New \ Sd^2 = \dfrac{(x_1+c -(\overline x+c))^2+ (x_2+c -(\overline x+c))^2 +...+ (x_3+c -(\overline x+c))^2}{n}}[/tex]
[tex]\mathbf{New \ Sd^2 = \dfrac{(x_1+c -\overline x+c)^2+ (x_2+c -\overline x+c)^2 +...+ (x_3+c -\overline x+c)^2}{n}}[/tex]
[tex]\mathbf{New \ Sd^2 = (x_1- \overline x)^2+ (x_2- \overline x)^2+ ... +(x_n- \overline x)^2}[/tex]
[tex]\mathbf{New \ Sd^2 = old \ sd^2}[/tex]
