The image above represents standard deviation. To calculate the 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)Â **andÂ **Probability of a failure in any single trial (q).**

The formula for calculating standard deviation:

Ïƒ = âˆš(npq)

Where;

Ïƒ = 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

Ïƒ = âˆš(npq)

So, Ïƒ = âˆš((14)(0)(1))

Ïƒ = âˆš(0)

Ïƒ = 0

Therefore, the **standard deviation** is **0.**

**Calculating the 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 are Given**

n = ^{Ïƒ2} / _{pq}

Where;

n = Number of Possible Outcomes in Any Single Trial

Ïƒ = 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?

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This implies that;

Ïƒ = Standard deviation = 5

p = Probability of a Success in Any Single Trial = 1

q = Probability of a Failure in Any Single Trial = 1

n = ^{Ïƒ2} / _{pq}

Then, n = ^{52} / _{1 x 1}

n = ^{25} / _{1}

n = 25

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

Read more:Â How to Calculate and Solve for Mean | Probability

**Calculating 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 are Given**

p = ^{Ïƒ2} / _{nq}

Where;

p = Probability of a Success in Any Single Trial

Ïƒ = 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;

Ïƒ = Standard deviation = 2

n = Number of Possible Outcomes in Any Single Trial = 2

q = Probability of a Failure in Any Single Trial = 1

p = ^{Ïƒ2} / _{nq}

Then, p = ^{22} / _{2 x 1}

p = ^{4} / _{2}

p = 2

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

Read more:Â How to Calculate and Solve for Success and Failure | Probability

**Calculating 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 are Given**

q = ^{Ïƒ2} / _{nq}

Where;

q = Probability of a Failure in Any Single Trial

Ïƒ = 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;

Ïƒ = Standard deviation = 3

n = Number of Possible Outcomes in Any Single Trial = 2

p = Probability of a Success in Any Single Trial = 1

q = ^{Ïƒ2} / _{nq}

q = ^{32} / _{2 x 1}

That is, q = ^{9} / _{2}

q = 4.5

Therefore, theÂ **probability of a failure in any single trialÂ **isÂ **4.5.**

**How to Calculate and Solve for Standard Deviation Using Nickzom Calculator**

Nickzom Calculator â€“Â **The Calculator Encyclopedia** is capable of calculating the standard deviation.

To get the answer and workings of the standard deviation using the **Nickzom Calculator â€“ The Calculator Encyclopedia.Â **First, you need to obtain the app.

You can get this app via any of these means:

**Web**Â â€“Â https://www.nickzom.org/calculator-plus

To get access to theÂ **professionalÂ **version via web, you need toÂ **register**Â andÂ **subscribeÂ **for**Â NGN 1,500Â **per**Â annum**Â to have utter access to all functionalities.

You can also try theÂ **demoÂ **version viaÂ https://www.nickzom.org/calculator

**Android (Paid)**Â â€“Â https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)**Â â€“Â https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)**Â â€“Â https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to theÂ **Calculator Map,Â **then click onÂ **Probability****Â **underÂ **Mathematics****.**

Now, Click on **Standard Deviation****Â **underÂ **Probability**

The screenshot below displays the page or activity to enter your values, to get the answer for the standard deviation according to the respective parameters which are the **Number of possible outcomes in any single trial (n), Probability of a success in any single trial (p)Â **andÂ **Probability of a failure in any single trial (q).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Number of possible outcomes in any single trial (n)** is **14**,** Probability of a success in any single trial (p) **is **0 **andÂ **Probability of a failure in any single trial (q)** is **1**.

Finally, Click on Calculate

As you can see from the screenshot above,Â **Nickzom Calculator**â€“ The Calculator Encyclopedia solves for the standard deviation and presents the formula, workings and steps too.