Question

use the five numbers 18, 15, 12, 13, and 12 to complete parts a) through e) below.

a) compute the mean and standard deviation of the given set of data.
the mean is \\(\bar{x} = 14\\) and the standard deviation is \\(s = 2.55\\).
(round to two decimal places as needed.)

b) add 25 to each of the numbers in the original set of data and compute the mean and the standard deviation of this new set of data.
the new mean is \\(\bar{x} = 39\\) and the new standard deviation is \\(s = 2.55\\).
(round to two decimal places as needed.)

c) subtract 10 from each of the numbers in the original set of data and compute the mean and the standard deviation of this new set of data.
the new mean is \\(\bar{x} = \\) and the new standard deviation is \\(s = \\).
(round to two decimal places as needed.)

Explanation:

Apply linear transformation to the mean

Using the Linear Transformations of Data and Mean Calculation knowledge points

$$
LATEXBLOCK0
$$

Apply linear transformation to the standard deviation

Using the Linear Transformations of Data and Sample Standard Deviation knowledge points

$$
LATEXBLOCK1
$$

Answer:

Subtract 10 from each of the numbers in the original set of data and compute the mean and the standard deviation of this new set of data.

The new mean is \(\bar{x} =\) <blank>4</blank> and the new standard deviation is \(s =\) <blank>2.55</blank>.