What is a Z-Score Table?

A chart or database containing pre-calculated values assigned to particular Z-scores is known as a Z-score table. Finding the probability that a random variable from a typical normal distribution will go below or above a specific Z-score is made easier.

Fundamentally, a Z-score, sometimes referred to as a standard score, measures how much a data point deviates from a distribution’s mean (average) by the number of standard deviations. The Z-score formula, Z = (X – μ) / σ, can be used to compute this deviation. The Z-score is represented by Z, the value to be standardized by X, the distribution mean by μ, and the spread of the data by σ, which is the standard deviation.

Z-Score Definition

Z score also referred to as a standard score, calculates how many standard deviations a data point deviates from the normal distribution’s mean (average).

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How to Calculate Z-Scores?

To calculate Z-Score using table, we can use the following steps:

Step 1: Identify the data point (X).

Step 2: Find the mean (µ) and standard deviation (σ).

Step 3: Substitute the coefficients in the formula.

Step 4: Calculate the Z-score.

Let’s consider an example for better understanding.

Example: If the class average on a math test is 65 with a standard deviation of 10, a student who scored 75 can calculate his Z-score as follows.

Solution:

Given: X = 75, µ= 65, and σ = 10

Using the formula for Z-Score.

Z = (X – µ)/σ

⇒ Z = (75-65)/10

⇒ Z = 1

Z Score Table is the table for determining the probability of a standard normal variable falling below or above a certain value. Z-score table, also known as a standard normal table or z-score Table, is a mathematical table that provides the area under the curve to the left of a z-score in a standard normal distribution. The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1.

The z-score table is used to find the probability that a random variable from a standard normal distribution will fall below a certain value. In this article, we will learn about the Z Score Table in sufficient detail and also learn how to use the Z Score Table in numerical problems.