Chapter 10, Problem 6PFA

To determine

To evaluate the statistics for the given situation

Answer to Problem 6PFA

Mean of the new data set can be found by adding 4 to the mean’s original data set value.

Explanation of Solution

Given information:

Data set vales are increased by 4.

Statistic will be increased by +4

The formula for mean is,

  $\overline{x}=\frac{{\displaystyle \sum x}}{n}$

Let the data set consists of x₁, x₂and x₃

Therefore, substituting in the formula.

  $\overline{x}=\frac{x_1^{}+x_2^{}+x_3^{}}{3}$ _______________ (1)

The new data is,

(x₁+4), (x₂+4), (x₃+4)

Hence, for mean,

  $\overline{x}\text{'}=\frac{(x_1^{}+4)+(x_2^{}+4)+(x_3^{}+4)}{3}$

Opening the brackets,

  $\overline{x}\text{'}=\frac{x1+4+x2+4+x3+4}{3}$

On solving,

  $\overline{x}\text{'}=\frac{x_1^{}+x_2^{}+x_3^{}+12}{3}$

So,

  $\overline{x}\text{'}=\frac{x_1^{}+x_2^{}+x_3^{}}{3}+\frac{12}{3}$

So,

  $\overline{x}\text{'}=\frac{x_1^{}+x_2^{}+x_3^{}}{3}+4$

Substituting (1),

  $\overline{x}\text{'}=\overline{x}+4$

Hence, Mean of the new data set can be found by adding 4 to the mean’s original data set value.