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# How to Calculate and Solve for Standard Deviation | Probability

Last Updated on January 7, 2020

The image above represents standard deviation.

To compute for standard deviation, three essential parameters are needed and these parameters are Number of possible outcomes in any single trial (n), Probability of a success in any single trial (p) and Probability of a failure in any single trial (q).

The formula for calculating standard deviation:

σ = √(npq)

Where;

σ = Standard deviation
n = Number of Possible Outcomes in Any Single Trial
p = Probability of a Success in Any Single Trial
q = Probability of a Failure in Any Single Trial

Let’s solve an example;
Find the standard deviation when the number of possible outcomes in any single trial is 14, the probability of a success in any single trial is 0 and the probability of a failure in any single trial is 1.

This implies that;

n = Number of Possible Outcomes in Any Single Trial = 14
p = Probability of a Success in Any Single Trial = 0
q = Probability of a Failure in Any Single Trial = 1

σ = √(npq)
σ = √((14)(0)(1))
σ = √(0)
σ = 0

Therefore, the standard deviation is 0.

Calculating for Number of Possible Outcomes in Any Single Trial when the Standard Deviation, the Probability of a Success in Any Single Trial and the Probability of a Failure in Any Single Trial is Given.

n = σ2 / pq

Where;

n = Number of Possible Outcomes in Any Single Trial
σ = Standard deviation
p = Probability of a Success in Any Single Trial
q = Probability of a Failure in Any Single Trial

Let’s solve an example;
Given that standard deviation is 5, the probability of a success in any single trial is 1 and the probability of a failure in any single trial is 1. Find the number of possible outcomes in any single trial?

This implies that;

σ = Standard deviation = 5
p = Probability of a Success in Any Single Trial = 1
q = Probability of a Failure in Any Single Trial = 1

n = σ2 / pq
n = 52 / 1 x 1
n = 25 / 1
n = 25

Therefore, the number of possible outcomes in any single trial is 25.

Calculating for Probability of a Success in Any Single Trial when the Standard Deviation, the Number of Possible Outcomes in Any Single Trial and the Probability of a Failure in Any Single Trial is Given.

p = σ2 / nq

Where;

p = Probability of a Success in Any Single Trial
σ = Standard deviation
n = Number of Possible Outcomes in Any Single Trial
q = Probability of a Failure in Any Single Trial

Let’s solve an example;
Given that standard deviation is 2, the number of possible outcomes in any single trial is 2 and the probability of a failure in any single trial is 1. Find the probability of a success in any single trial?

This implies that;

σ = Standard deviation = 2
n = Number of Possible Outcomes in Any Single Trial = 2
q = Probability of a Failure in Any Single Trial = 1

p = σ2 / nq
p = 22 / 2 x 1
p = 4 / 2
p = 2

Therefore, the probability of a success in any single trial is 2.

Calculating for Probability of a Failure in Any Single Trial when the Standard Deviation, the Number of Possible Outcomes in Any Single Trial and the Probability of a Success in Any Single Trial is Given.

q = σ2 / nq

Where;

q = Probability of a Failure in Any Single Trial
σ = Standard deviation
n = Number of Possible Outcomes in Any Single Trial
p = Probability of a Success in Any Single Trial

Let’s solve an example;
Given that standard deviation is 3, the number of possible outcomes in any single trial is 2, the probability of a success in any single trial is 1. Find the probability of a failure in any single trial?

This implies that;

σ = Standard deviation = 3
n = Number of Possible Outcomes in Any Single Trial = 2
p = Probability of a Success in Any Single Trial = 1

q = σ2 / nq
q = 32 / 2 x 1
q = 9 / 2
q = 4.5

Therefore, the probability of a failure in any single trial is 4.5.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the standard deviation.

To get the answer and workings of the standard deviation using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator