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Z Score Calculator

The 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.

How to use the Z - score calculator?

The use of a z - score calculator is easy and simple here are the steps you need to follow:

Select the data type from the drop-down menu.
Put the value of “Data Point(s) X”.
Put the value of “Population Mean(μ)”.
Put the value of “Population Std Dev(σ)”.
Click on the “calculate” button for the step-by-step result of (selected type of data) z-score.
Click on the “reset” button for more inputs.

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:

Z score 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 Std Dev (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