What Is a Z-Score? A z-score, or z-statistic, is **a number representing how many standard deviations above or below the mean population the score derived from a z-test is**. Essentially, it is a numerical measurement that describes a value’s relationship to the mean of a group of values.

Z-score indicates **how much a given value differs from the standard deviation**. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.

In this case, because the mean is zero and the standard deviation is 1, the Z value is **the number of standard deviation units away from the mean**, and the area is the probability of observing a value less than that particular Z value.

Z-score is also known as standard score gives us an idea of how far a data point is from the mean. It **indicates how many standard deviations an element is from the mean**. Hence, Z-Score is measured in terms of standard deviation from the mean.

The z-score is particularly important because **it tells you not only something about the value itself, but also where the value lies in the distribution**.

Z-scores are important because **they offer a comparison between two scores that are not in the same normal distribution**. They are also used to obtain the probability of a z-score to take place within a normal distribution. If a z-score gives a negative value, it means that raw data is lesser than mean.

**From the use of “Z” in Z distribution, another name for normal distribution**.

Z scores (Z value) is **the number of standard deviations a score or a value (x) away from the mean**. In other words, Z-score measures the dispersion of data. Technically, Z-score tells a value (x) is how many standard deviations below or above the population mean (µ).

While data points are referred to as x in a normal distribution, they are called z or z scores in the z distribution. **A z score is a standard score that tells you how many standard deviations away from the mean an individual value (x) lies**: A positive z score means that your x value is greater than the mean.

Positive Z-scores result from values that are above the mean, and negative Z-scores are from values below the mean. **The greater a Z-score’s absolute value, the more extraordinary is the data point’s deviation from the mean**.

In general, **a Z-score below 1.8 suggests a company might be headed for bankruptcy**, while a score closer to 3 suggests a company is in solid financial positioning.

Z-scores tell you how many standard deviations from the mean each value lies. Converting a normal distribution into a z-distribution **allows you to calculate the probability of certain values occurring and to compare different data sets**.

Z is **the value from the table of probabilities of the standard normal distribution for the desired confidence level** (e.g., Z = 1.96 for 95% confidence) E is the margin of error that the investigator specifies as important from a clinical or practical standpoint. σ is the standard deviation of the outcome of interest.

So, the general form of a confidence interval is: point estimate + Z SE (point estimate) where Z is **the value from the standard normal distribution for the selected confidence level** (e.g., for a 95% confidence level, Z=1.96). In practice, we often do not know the value of the population standard deviation (σ).

A positive z-score says the data point is above average. A negative z-score says the data point is below average. A z-score close to 0 says the data point is close to average. **A data point can be considered unusual** if its z-score is above 3 or below −3 .

Since z-scores are a measure of the number of standard deviations (SDs) between a value and the mean, **they can be used to calculate probability by comparing the location of the z-score to the area under a normal curve either to the left or right**.

A normal BMD Z-score ranges from -2.5 to 2.5 [3, 4]. A normal Z-score means that you have a similar BMD to other healthy people in your age group. A lower Z-score means **your BMD is lower** and a higher Z-score means it’s higher.

When considering the sampling distribution, Z-score or Z-statistics is defined as **the number of standard deviations between the sample mean and the population mean (mean of the sampling distribution)**. Note that the sampling distribution is used in the hypothesis testing technique known as Z-test.

The critical z-score values when using a 95 percent confidence level are **-1.96 and +1.96 standard deviations**.

The value of z* for a confidence level of 95% is **1.96**.