What are Z-Scores?
Z-scores are great as these allow us to avoid the hassle of memorizing algebra rules which everyone finds a neck pain to remember. There are many names of z-scores that one can interact with like standard score, z-value and normal score. Basically, z-score describes the dimensionless amount that is utilized to show the marked, fragmentary, number of standard deviations by which an occasion is over the mean worth being estimated. Qualities over the mean have positive z-scores, while values underneath the mean have negative z-scores.
In simple words, z-scores allow us to compare individual values or scores on a single distribution as long as we have mean and standard derivation where the mean=0 and standard derivation is +1 or -1 etc. If you are finding a calculating Z-score a hassle then our Z-score calculator allows you to calculate any Z-score value without any hassle. Let’s find out more about this calculator along with other terms in Z-score.
Z Score Calculator
Like many other mathematical or statistical problems, calculating z-score by hands is quite a hassle and time taking the job. But like our many other online calculators, this Z score calculator is also a specimen of itself. You cannot find a better z score calculator than this because of its usability and user interface. This Z Score calculator works on the basic formula and principles of Z–score to deliver the most accurate and acceptable results.
Z Score Formula
As per the definition of Z-Score, it can be calculated by subtracting the population mean from the raw score. You can also consider data point in question such as calculating test score, height, age etc. In this case, the dividing difference will be the population standard deviation. The same formula is utilized by our Z score calculator.
$$z = x – μ / σ$$
Where x is the raw score, μ is the populace means, and σ is the populace standard deviation.
The z-score has various applications and can be utilized to play out a z-test, compute forecast interims, process control applications, correlation of scores on various scales, and that's only the tip of the iceberg. You can find as many applications of Z-Score as you want.
The Standard Normal Distribution (SND) in Z-Score
The standard typical or normal distribution is an extraordinary sort of ordinary circulation for a nonstop arbitrary variable Z with a typical measurement.
This is the distribution whereupon our z scores convert to, maybe, if you will.
In the standard normal distribution
- SD = 1 and mean =0
In the SND we also have the formula to convert any “raw score” to a z score. The most widely recognized Z score equation is for populace information beneath yet we have more
$$z = x – μ / σ $$
Z score Table “Right Tail Z-Score Table” or Z-Table
A z-table, otherwise called a standard ordinary table or unit typical table is a table that comprises of standardized values that are utilized to decide the probability that a given measurement is beneath, above, or between the standard ordinary distributions.
The table beneath is a right-tail z-table. In spite of the fact that there are various kinds of z-tables, the right-tail z-table is usually what is implied when a z-table is referenced. It is utilized to discover the zone between z = 0 and any positive worth, and reference the zone to one side hand side of the standard deviation bend.
Solved Problems of Z-Score
Example 1:For a distribution with a μ = 85 and σ = 5, find
What is the Z-score for X=85?
As per Z Score formula, Z = 85 – 85 / 5 = 0 / 5 = 0
What is the Z-Score for X = 90?
As per Z Score formula, Z = 90 – 85 / 5 = 5 / 5 = 1
You can find Z-Score of any term having the given values using Z Score Formula
How to Calculate Z-Score?
Calculating Z-score using this Z score calculator is one of the easiest jobs to do. You only need to perform the following steps to calculate the Z score using this calculator.
- Add “Experimental Result” in the First Field
- Add “Mean Value” in the Second Field
- Add “Standard Derivation Value” in the third Value
- Click on the “Calculate” Button
You will get your desired results within a few seconds after clicking on the calculate button making this z score calculator hassle-free to use.