What is the Z-Score?

Z Score

The standard score, or the Z-score in excel, is a way to calculate the difference between the actual score and the mean in standard deviation units. It also allows us to compare two examples from different populations. The z-value can be negative or positive. A negative z-score means that the value is less than the arithmetic value, and a positive z-score means that our value is greater than the arithmetic value. The Z-Score is calculated by subtracting the mean value of the data set from the data set to be calculated and dividing it by the standard deviation of the data set.

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What is the Z-Score used for in our everyday life?

Not everyone is a statistician or mathematician, but everyone deals with data sets almost every day. Whether it’s your screen time, the final exam, the class, or how much you spent on clothes last year. It means that we also use statistical measures such as the mean or the deviation.

But where should you use the z-score?

1. We can use it by comparing two different datasets with different distributions.

We have two chefs who know how to make soufflé. Let’s say our first cook is called Sasha and the other is David. David took part in a cooking competition and got a score of 472 out of 500. Sasha also took part in this type of competition and got a score of 82 out of 100. Now we have to decide who was the most positive. But how? David’s score is highest than Sasha’s, but we can’t compare them like that. In these situations, we convert the raw score to z scores. This way we can calculate who did the best in the competition.

In the competition that David participates in, the mean was 392, and the standard deviation was 100. To calculate the standard score, we subtract the mean 392 from David’s score of 472 and divide it by the standard deviation. The correct equation for this is “472 -392 / 100,” which is +0.08. David’s score is 0.08, a standard deviation above the mean.

In Sasha’s contest, the mean was 52, and the standard deviation was 30. We are now applying the same formula that we use for David’s contest. We deduct the mean from the score and divide it into the standard deviation. The equation for this is “82 -52 / 30”. Sasha’s z score is +1. It means Sasha is one standard deviation above the mean.

Now that we can easily compare the score of David and Sasha. David was 0.8 standard deviation above, & Sasha is 1.0 standard deviation above average. It means that Sasha is a better soufflé baker than David. That’s what the statistics tell us. But maybe we shouldn’t make up our minds without trying both.

“Another place where the default is used is to measure the growth of children in the world. It is used to compute weight and height for age. Children who are below the standard deviation of -2 or -3 are diagnosed with malnutrition. ”

Tip: Always add less or more to the z-values ​​and convert them after 0, x to two-digit numbers. And you should always add 0 before the decimal point if the value is less than 1. For example, 0.8798 ci should be converted to +0.88 above the mean.

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2. Two compare the frequency of a score

The Z-scale I just created can tell me how many candidates are getting the Sasha or David score. When I look at the Z scale, I am told that the people who took David’s score are more than those who took Sasha’s score because most of the data will capture a standard deviation below or above the mean.

3. It allows us to guess the score

The Z scale can be used to determine whether Sasha or David is likely to get their scores. We can use it in hypothetical measurements. “But how do converting raw data to z-scores help us compare those? It is because the z-score distribution always has a mean of 0 and a standard deviation of 1.00. Although the original distribution is abnormal, the mean is 0, and the standard deviation is 1.00. It helps us standardize and compare two different data sets, even though they were measures differently, as in our example.

Most of the z-score distribution data fall between standard deviations of less than and more than 1.00 from the mean. There are fewer data between 2 standard deviations above and below the mean, and it is scarce to find data greater than plus and minus three standard deviations.

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Why do we need the Z-Score?

As we see from the examples above, we need a z score to compare two different data sets by standardizing each type of measure. By converting your data to Z-Score, your data is fundamentally gets resize and standardize. For this reason, it is also known as the standard score. We can think of a Z-Score as a cookie-cutter. We can cut cookie dough or styrofoam, but both still look like the gingerbread man.

How do you mathematically calculate the Z value?

The Z score, or standard score, is calculate by dividing the data point minus the man by the standard deviation. But what do these terms mean? In fact when we collect individual information about something, we call it the group, dataset, or population dataset. In this article, all the data is numeric, but data can be of any real-life information. A single datum can be called a data point or individually, and I’m going to refer to it anyway so that you don’t get confused.

The average value is “average” in the statistics. It calculates by adding all data and dividing by the number of data.Therefore I will give an example, and I powerfully advise you to rely on me during this time. For example, let’s say we’re curious about how many hours we spend in front of the screen each day, and we’ve recorded our daily screen time for a week 2, 2, 5, 3, 7, 1, and 1. We add all of these numbers, and the result is 21. We have seven individual data points, so we divide 21 by seven and find the result 3. You spend an average of 3 hours per week in front of the screen.

Another thing that we need to find to find the z-score is the standard deviation. Standard deviation is an arithmetical term uses to determine the deviation between the mean and the actual data. A slight standard deviation means that the sensitivity of the data is consistent and standard. The data points are close together. A high standard deviation means that the data set is inconsistent, unexpectedly, and sometimes unreliable. It means that the data set people are not close to one another but are distributes over a series of numbers.

To calculate the standard deviation, we subtract all the numbers from the mean and square them to avoid negative values. We’ll square these numbers and divide them by one less than the number of people in our data set. In our Screen Time example, we can explain this as follows:

The average is 3, so three is subtract from every data point. We occupy 2 hours in front of the screen on Monday, which means “2 -3 = -1”. Now we have squared the result “-1” and get the number 1.

Therefore, We use the same formula for every person in our data set. Then we add these numbers and get the result of √30. We’re going to divide it into minus the number of data points of 6. It brings us to the end of 0.9. It is our standard deviation value.

Please see our article to Calculate the Standard Deviation in Excel for more information on the standard deviation and calculate it in Excel. Now that we have the mean and standard deviation, we can calculate the Z-value.

Continuing with the Screen Time example, we’ll calculate the Z-score for Monday. We need to subtract the mean of our data point and divide it into the standard deviation value. For us this means “2 -3 = -1”. Next we divide -1 to 0.9 which is our usual deviation value “-1 / 0.9 = -1.1”. The result is -1.1. It means that our screen time on Monday is greater than one and less than two standard deviations from the mean.

 

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