Z-Score Table

A Z-score is described as the number of standard deviations from the mean. A data point present in the Z-score is the calculation of how many standard deviations above or below the mean. A standard score is a raw score as the Z-score and is placed on a normal distribution curve. Z-scores are the scores that are capable of ranging from -3 to +3 standard deviations. The following is the graphical representation of the same,

This can also help us determine the common difference or distance between a value and a mean value. When a variable is standardized, its means become zero whereas its standard deviation becomes one. To calculate the Z-score, the following method is followed. The basic Z-score formula for a sample is,

z = (x – ) / σ

where,

– mean value

x – test value

– standard deviation

Or another form is used, which is given below,

zi = xi -  x S

where,

x = sample mean

S = sample standard deviation

Z-score formula - Standard error of the mean

It is when you have multiple samples and would want to define the standard deviation of those sample means, then, the following Z-score formula is used:

z = (x – ) / ( / n)

From this formula, the Z-score tells how many standard errors are there between the sample means as well as the population means.

Z-score tables – Area under a normal curve

This table is utilized to find a specific area under a normal curve. At first, the Z-score of the data value has been found followed by using a Z-score table to identify the area. This Z-score table shows the area percentage (or percentage of values) to the left of a provided Z-score on a normal distribution.

The following are the two types of Z-score tables:

1. Positive Z-scores table: When the observed values are above the mean of total values, then the table is said to have a positive Z-score.
2. Negative Z-scores table: Negative Z-score values represent the observed Z-score value, which is below that of the mean of total values.

The main purpose of this table is to identify the standard normal deviation, which is considered to have a mean of 0 and a standard deviation of 1.

• In the table’s first column, one can easily identify the number of the standard deviations which are placed either above or below the mean value to one decimal place. The row label contains both the integer part and the first decimal of the Z-score.
• The part that is capable of denoting the Z-score which is the hundredth value that is situated across the topmost row of the table.
• Then there lies an intersecting point for the columns and rows. This point indicates the area under the normal curve or the probability.