Question

Find the standard deviation of the following data. Round your answer to one decimal place. x 0 1 2 3 4 5 P(X

Answer 1

Answer:

$\sigma = 1.8$

Step-by-step explanation:

Given

$\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}$

Required

The standard deviation

First, calculate the expected value E(x)

$E(x) = \sum x * P(x)$

So, we have:

$E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2$

$E(x) = 2.7$

Next, calculate E(x^2)

$E(x^2) = \sum x^2 * P(x)$

So, we have:

$E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2$

$E(x^2) = 10.5$

The standard deviation is:

$\sigma = \sqrt{E(x^2) - (E(x))^2}$

$\sigma = \sqrt{10.5 - 2.7^2}$

$\sigma = \sqrt{10.5 - 7.29}$

$\sigma = \sqrt{3.21}$

$\sigma = 1.8$ --- approximated