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 = ^{σ}^{2} / _{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 = ^{σ}^{2} / _{pq}

n = ^{5}^{2} / _{1 x 1}

n = ^{25} / _{1}

n = 25

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

Continue reading How to Calculate and Solve for Standard Deviation | Probability