Created By : Vaibhavi Kumari
Reviewed By : Phani Ponnapalli
Last Updated : Apr 03, 2023

Get this super handy free online standard deviation probability calculator tool to determine the probability of standard deviation. Enter the values in the input fields and press the calculate button and get the answers instantly.

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### Standard Deviation Probability Formula

Standard deviation in probability is nothing but the average distance of a random variable which is taken from the mean. Standard deviation is denoted by 'σ'. To find the probability of standard deviation we use a certain formula, let us look into it:

σ = √Σ(xi-μ)2 * P(xi)

Where,

μ is the mean.

P is the pobability.

xi is the ith value.

P(xi) is the probability of ith value.

### Steps to Calculate Standard Deviation Probability

Following are the steps to calculate the probability of standard deviation.

• Takedown all the values in the problem.
• Apply the formula to find the probability of standard deviation.
• Then, after simplifying it you will get the value you need.

### Standard Deviation Probability Solved Example

Example: Find the probability of standard deviation for the following data.

Goals(x) Probability P(x)
1 0.56
2 0.16

Solution:

Given values are x =1, 2 and P(x) = 0.56, 0.16

First, we need to calculate the mean for the above table values.

Mean (μ ) = 1 * (0.56) + 2 * (0.16) = 0.88.

Now, calculating (xi-μ)2 * P(xi)

P(0.56) = (1-0.88)2 * 0.56 = 0.008064.

P(0.16) = (1-0.88)2 * 0.16 = 0.002304

Formula, σ = √Σ(xi-μ)2 * P(xi)

Standard deviation probability = √(0.008064 + 0.002304) = 0.101

Therefore, the standard deviation of probability is 0.101

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### FAQs on Standard Deviation Probability Calculator

1. How to find the standard deviation probability?

We can find the probability of standard deviation using σ = √Σ(xi-μ)2 * P(xi)

2. How to use the standard deviation probability calculator?

Just you need to enter the input values in the input fields and click on the calculate button to get the answers in a blink of an eye.

3. What is standard deviation in simple words?

Standard deviation is the average distance of the random variable which is taken from the mean.