Usually, when you're doing research about groups of people or objects, you will use both descriptive and inferential statistics. ​

There are many occasions when you want to analyze a specific group but you simply can't have a sample of the entire population. Unlike on the previous example, you wanted to analyze the performance of 100 students, in this case, you might want to measure the performance of all the students in a country. Since it's not doable to collect all the data, you need to choose a smaller sample of students, which will represent all the students in that country. 
 
And this is where the inferential statistics have their crucial role. They refer to the techniques that you use that allow you to use the samples to make generalized comments regarding the entire population. So, as you understand, it's very important to be careful when selecting the sample that represents the population. It needs to be as accurate as it can or the results won't represent the truth. 
 
The descriptive and inferential statistics have one thing in common: they both rely on the same data. However, while the descriptive statistics only relies on this particular data, the inferential statistics relies on this data to make general conclusions about a larger population. 
 
In order to analyze the data, both descriptive and inferential statistics need to rely on some functions of the data. In the case of the descriptive statistics, it tends to rely on some classic statistics like the mean, standard deviation, min, max, skew, median, and kurtosis. In the case of the inferential statistics, they tend to use some classic statistics like the z score, t score, F-ratio, among others. 
 
So, which one should you choose to use? You may need to use both types of statistics and the answer depends on the purpose of your research. For example, when a company is trying to show if a new medicine will be able to help patients in the future, it's in their best interest that they use inferential statistics. If they decide to use descriptive statistics, they won't be able to withdraw any conclusions regarding the population in general but simply regarding the patients that participated in the study. ​

The z score, also known as the standard score, allows you not only to compare two scores from different normal distributions as it also allows you to calculate the probability of one specific score to occur within the normal distribution.
 
The z score, by taking into account the standard deviation (SD) of the group, standardizes a score with respect to the other scores in the group. When you convert a raw score into a z-score, you'll get a number between 0 (the mean) and 1 (the standard deviation). Basically, what you will be doing is that you'll be defining each score you have in terms of how far away each one is from the group mean.

Main Advantages Of Using Z-Scores:
 
There are mainly two advantages why so many different organizations use the z-scores:
 
-- Clarity: At a single glance, you can easily see how bad or good a score is when compared to the entire group.
 
-- Comparison: Being able to compare scores that are measured on different scales is definitely a huge advantage.
 
 
Results From The Z-Scores:
 
When you are looking at a z-score table, you have three distinct areas:
 
-- The Area Under The Curve: Looking at this part of the table will allow you to see the different properties of the normal distribution. So, you'll be able to see how many scores are under pre-determined limits as well as you'll be able to calculate the probability of a specific score to occur.
 
-- The Area Between The Mean And The Z: This area corresponds to the area under the curve, and that is between the mean and the z-scores. In this area, you can see the proportion of scores that are located between the mean and any given z-score.
 
-- The Area Beyond Z: In this area, you'll see the proportion of the scores that are greater than any given z-score.
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Calculating The Z-Scores:
 
The easiest way to calculate a z-score is to use a z score calculator. However, in case you're interested in knowing how to calculate it by hand, you just need to find the difference between the score and the mean score, which tells you how far away the score is from the average score, and divide it by the standard deviation. Then you can use a z score table to find a probability.
 
There's no question that is far more effective and time-saving using a z score calculator.