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)
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.
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 ) +
Step 3: Take the square root of Step 2:
σ = √ 0.75 = 0.8660254.
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