Main>Binomial Distribution>Standard deviation binomial distribution

## Standard Deviation Binomial Distribution: Overview

A binomial distribution is one of the simplest types of distributions in statistics. It’s a type of distribution where there is either success, or failure. For example, winning the lottery: or not winning the lottery. You can find the standard deviation binomial distribution in two ways:

- With a formula
- With a probability distribution table (scroll down for the steps)

The formula to find the standard deviation binomial distribution is:

Watch the video or read the steps below:

**Sample question:** Find the standard deviation binomial distribution for flipping a coin 1000 times to see how many heads you get.

Step 1: Identify n and p from the question. N is the number of trials (given as 1000) and p is the probability, which is .5 (you have a 50% chance of getting a heads in any coin flip).

*At this point you can insert those numbers into the formula and solve. If formulas aren’t your forte, follow these additional steps:*

Step 2: Multiply n by p:

1000 * .5 = 500.

Step 3: Subtract “p” from 1:

1 – .5 = .5.

Step 4: Multiply Step 2 by Step 3: 500 * .5 = 250.

Step 5: Take the square root of Step 4:

√ 250 = 15.81.

*That’s it!*

## Standard Deviation of Discrete Random Variables

With discrete random variables, sometimes you’re given a probability distribution table instead of “p” and “n”. As long as you have a table you can calculate the standard deviation of discrete random variables with this formula:

**Sample question: **Find the standard deviation of the discrete random variables shown in the following table which represents flipping three coins:

Step 1: Find the mean (this is also called the expected value) by multiplying the probabilities by x in each column and adding them all up:

μ = (0 * 0.125) + (1 * 0.375) + (2 * 0.375) + (3 * 0.125) = 1.5

Step 2: work the inner part of the above equation, without the square root:

((0 – 1.5)^{2} * 0.125 ) +

((1 – 1.5)^{2} * 0.375 ) +

((2 – 1.5)^{2} * 0.375 ) +

((3 – 1.5)^{2} * 0.125 ) +

= 0.75

Step 3: Take the square root of Step 2:

σ = √ 0.75 = 0.8660254.

*That’s it! *

Questions? Post them on our FREE statistics forum. Our stats guy will be happy to answer your questions (he’ll even tackle homework problems!).

With this section its okay until you get down to the 4th step and then I am lost although this article did help me figure out how to finish the problem. So I am glad that they do have this information in here for us to look at so we have something to fall back on.

It would be helfpul if you provived the results next to each step so we can work the problem as we follow each step and make sure we are calculating correctly.

I wish I would have read this information before I did the long walk to ace for help! I chart is a lot of help but I agree the steps are a little confusing, just read over them two times and it will make sense.

This was very helpful. I was confused on the probablility distribution chart

Your explanation here is much simpler and easier to follow than the one given in the book. I agree, it’s great to have this blog to fall back on.

This blog did help me to understand standard deviation better, but it would be better if the problem was written out with each step. I think this would help all us visual learners!

This blog really helped me with the probability chart because I was really confused for the longest time as I am sure you are well aware of. I really like looking on this because I feel like I get a better understanding.

This example is very helpful because it has the links to other problems that we have already covered. We learn things in previous sections but it is always nice to be able to go back for a refresher.

This example was very helpful and It helped me with ch8 hw.

it is a good example.it help me a loot

it is a good example.it help me alooot.