Statistics How To

Standard Deviation Binomial Distribution in Easy Steps

Main>Binomial Distribution>Standard deviation binomial distribution

Standard Deviation Binomial Distribution: Overview

standard deviation binomial distribution

A coin toss can be a binomial experiment.


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:

  1. With a formula
  2. With a probability distribution table (scroll down for the steps)

The formula to find the standard deviation binomial distribution is:
standard deviation binomial distribution

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:
standard deviation discrete random variable

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

standard deviation discrete random variable

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!).

11 thoughts on “Standard Deviation Binomial Distribution in Easy Steps

  1. Lisa Barcomb

    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.

  2. Rebecca Gamble

    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.

  3. Donna Allen

    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.

  4. Catherine Flanagan

    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!

  5. Lisa Barcomb

    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.

  6. angie widdows

    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.