What is a z-score and how to find it?

In statistical studies, we have to analyze large data sets, and for that purpose we need to work out mean and standard deviation. What do we need to compare a particular value with the mean? We can’t just compare each value in a large pile of information. 

There is an easy way out by using a great score called z-score. In order to use it, we must calculate mean and standard deviation. In this article, you will learn more about these scores and the possible ways to calculate it. Now, let’s get started.

Z-score: 

A z-score or a standard score is a value that indicates the position of a data set in relation to the mean. In other words, it tells us how far a value is placed from the mean. More precisely, it is a measure of the number of standard deviations placed below or above the mean.

We can also place this score on a normal distribution curve. It ranges from -3 to +3 standard deviation. When we say it +3, it means the score would reside to the far right of a distribution curve. Contrary to this, the -3 would fall on the far left side, as shown in the graph;

Image result for z score distribution curve"

As we mentioned earlier, z-scores are the tools to compare data values of sample to the normal population. Outcomes from trials or surveys have hundreds and even thousands of expected results. 

These large data values can often prove worthless and time consuming. For instance, in a survey of a particular population, someone’s age is 55 years. 

This information is not enough, we have to compare it to the general population’s average age. But, we can’t just compare it by looking at the enormous data table. Here, z-score will prove useful and can easily compare it with the mean.

How to find a z-score?

Now, to find how many standard deviations, a data point is away from the mean, we can use the following methods;

1) Z-score Formula:

To find a standard score we need three values; the data point(x) to be compared, the mean and the standard deviation.

               Z = (x – μ) / σ

Example: Let’s suppose, you have to compare an exam score of 180. The mean of the exam is 140, and a standard deviation of 20.

              Z= (180 – 140) / 20

              Z= 2 (It means the score is 2 standard deviations above the mean)

2) Use of excel:

An easy way to compute the standard score is by using the Microsoft excel, just use the; AVERAGE and STDEV.S formulas to find the score.

Function=(DataPoint-AVERAGE (DataSet))/STDEV(DataSet)

The first statistical value needed is the ‘mean’ and Excel’s AVERAGE function computes that value. It simply sums up all the values and divides by the number of entries.

The next value is the deviation; and the excel has two functions for that;

STDEV.S: This function calculates the standard deviation while considering the data as a sample, collected from the general population.

STDEV.P: This function considers the data as a whole population.

3) Use of Online tools:

The easiest way to calculate the z-score is through an online tool, there are dozens of online gizmos that are specifically designed for this purpose. No need to remember the formulas, just feed it with the requirements.

All you need to do is enter the required values in the fields and press calculate, it provides the desired results with speed and precision. If you are interested, try the z-score calculator.

In the end, we are optimistic that this article will help you understand the basics, and assist you in solving problems related to statistical data. Good luck! 

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