 # Confidence Interval Calculator

To use confidence interval calculator, enter the required information and click the calculate button

Formula:
x̄ ± Z   sn

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## Confidence Interval Calculator

Confidence interval calculator is used to find the confidence interval of the data set and group data. This calculator also finds the population mean and standard deviation under the particular sample size.

## What is a Confidence Interval?

A confidence interval is a range of values in a population parameter such as a mean, proportion, or another statistical measure that lies in a certain confidence level. It is a statistical estimate of the uncertainty or variability related to an estimated parameter depending on sample data.

### Confidence Interval Formula

Confidence interval = [x̄ ± Z S]/n

Where,

• = Mean value of the data,
• Z = Confidence level of Statistical data,
• S = Standard Deviation,
• n = sample size of data.

## How to calculate the confidence interval?

Example

Find the confidence interval for a given data.

Confidence level = 85%, mean = 15, Standard deviation = 12, Sample Size = 4.

Solution:

Step 1: Take the given values.

Z = Confidence level = 85%,

x̄ = mean = 15,

S = Standard deviation = 12,

n = Sample Size = 4.

Confidence interval =?.

Step 2: Write the formula to find the confidence interval.

Confidence interval = [x̄ ± Z S/n]

Step 3: Put the values in the above formula

CI = [15 ± 0.85 (12)]/4

CI= [15 + 0.85 (12)]/4      or    CI = [15 - 0.85 (12)]/4

CI = [25.2]/4                    or     CI= [4.8]/4

CI = 6.3                            or     CI = 1.2

If mean = 15 , confidence level =  85%,  CI = [1.2 , 6.3]

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