Question

use the following distribution to complete parts (a) through (d) below.

1, 4, 7, 12, 11

a) compute the mean and standard deviation of the distribution.

the mean is 7.

the standard deviation is .
(round to the nearest hundredth as needed.)

Explanation:

Calculate the mean of the distribution

Using the Mean Calculation knowledge point

$$ \bar{x} = \frac{1 + 4 + 7 + 12 + 11}{5} = \frac{35}{5} = 7 $$

Calculate the squared deviations from the mean

Using the Sample Standard Deviation knowledge point

$$
LATEXBLOCK0
$$

Sum the squared deviations

Using the Sample Standard Deviation knowledge point

$$ \sum (x_i - \bar{x})^2 = 36 + 9 + 0 + 25 + 16 = 86 $$

Compute the sample standard deviation

Using the Sample Standard Deviation knowledge point

$$
LATEXBLOCK1
$$

Rounding to the nearest hundredth gives \(4.64\).

Answer:

The standard deviation is <blank>\(4.64\)</blank>.