Question

In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.
4, 13, 5, 14, 10
(a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to one decimal place.)

(b) Add 3 to each data value to get the new data set 7, 16, 8, 17, 13. Compute s. (Enter your answer to one decimal place.)

Answer 1

Answer:

a) s = 4.6

b) s = 4.6

Step-by-step explanation:

We are given the following in he question:

a) 4, 13, 5, 14, 10

We have to calculate sample standard deviation.

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{46}{5} = 9.2$

Sum of squares of differences = 82.8

$s = \sqrt{\dfrac{82.8}{4}} = 4.6$

b) Adding three to each observation

7, 16, 8, 17, 13

$Mean =\displaystyle\frac{61}{5} = 12.2$

Sum of squares of differences = 82.8

$s = \sqrt{\dfrac{82.8}{4}} = 4.6$

Thus, the two standard deviation are same.