Z Score Calculator is a statistical tool that assistances in standardizing data by altering it into a normal distribution. It compares data points from several datasets to create their relative placements. The Z Score calculates the distance between a data point and the dataset's mean in standard deviations.

## What is the z-score?

The Z score is a statistic that indicates, in terms of standard deviations, how distant a data point is from the dataset's mean. Thanks to its assistance in standardizing data, we can compare data points across various datasets.

### The formula of the z-score:

Calculating the z score needs the following formula:

Where:

- The standard score value is
**Z**. - The data point's value is
**X**. - The Population mean value is
**µ**. - The Population Std Dev value is (σ
**)**.

## Uses of Z-score:

Generally, the z-score is used to measure the deviation value from the mean of the data set We use the Z-score in many fields like finance, engineering, medicine, psychology, etc.

**In finance**, it is used to measure the solvency of corporations.**In engineering**, it is used to fix a product's or a process's quality.**In medicine**, it is used to identify conditions such as malnourishment and growth disorders.**In psychology**, it is used to analyze knowledge and academic disabilities.- It’s used in identifying outliers, testing hypotheses, monitoring processes, and controlling quality.

## Example section:

In this section, we’ll solve the example to gain a more complete understanding of this topic.

**Example 1:**

Find the Z-score value when the sample mean is x̄ = *48*, Sample Size n = 12, the population mean μ = 12, and Population Standard deviation (σ) = 8

**Solution:**

**Step 1: **Extract the data

x̄ = 48

μ = 12

σ = 8

n = 12

**Step 2: **Formula

**Z = (x̄ - μ) / (σ / √n)**

**Step 3: **Put values in the formula,

Z = (48 - 12) / (8 / √12)

Z = (36 / 2.3094010767585)

Z = 15.58846