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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
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.
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.
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.