The instersection of the two is the answer we’re looking. Once you have mapped these two values, find the interesection of the row of the first two digits and column of the second decimal value in the table. Once you have that, go alongside the X-axis on the topmost row to find the value of the digits at the second decimal position (.06 based on Eric’s Z score) Traverse horizontally down the Y-Axis on the leftmost column to find the find the value of the first two digits of your Z Score (0.5 based on Eric’s Z score). Let us understand using the example we’ve chosen with Eric’s Z score of 0.56
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Now that we’ve picked the appropriate table to look up to, in the next step of the process we will learn how to map our Z score value in the respective table. Now that we have Eric’s Z score which we know is a positive 0.56 and we know which corresponding table to pick for it, we will make use of the positive Z-table (Table 1.2) to predict how good or bad Eric performed compared to his batch mates.
Similarly, to find the area on the right of the mean, you will have a positive Z Score and use a positive Z Table. To find the area on the left of the mean, you will have a negative Z Score and use a negative Z Table. What we are basically establishing with a positive or negative Z Score is whether your values lie on the left of the mean or right of the mean. That is choosing between using the negative Z Table and the positive Z Table depending on whether your Z score value is positive or negative.
Once you have the Z Score, the next step is choosing between the two tables. In the above example, we derive that Eric’s Z-score is 0.56.
To map a Z score across a Z Table, it goes without saying that the first thing you need is the Z Score itself. Once we have the Z Score which was derived through the Z Score formula, we can now go to the next part which is understanding how to read the Z Table and map the value of the Z Score we’ve got, using it. Z Score = (Observed Value – Mean of the Sample)/standard deviation To find out the Z score we use the formula Using the above data we need to first standardize his score and use the respective z-table before we determine how well he performed compared to his batch mates. Let’s find out how well Eric scored compared to his batch mates. The average score for the batch was 700 (µ) and the standard deviation was 180 (σ). Eric scored 800 marks (X) in total out of 1000. Q: 300 college student’s exam scores are tallied at the end of the semester. Let us understand how to calculate the Z-score, the Z-Score Formula and use the Z-table with a simple real life example. Understanding how to use the Z Score Formula with an example Similarly, if we have the standard score provided and are missing any one of the other three values, we can substitute them in the above formula to get the missing value. When we do not have a pre-provided Z Score supplied to us, we will use the above formula to calculate the Z Score using the other data available like the observed value, mean of the sample and the standard deviation. The Z Score Formula or the Standard Score Formula is given as Z Score helps us compare results to the normal population or mean The Z Score Formula Whereas if Z Score = 0, it means the value is identical to the mean.Ī Z Score can be either positive or negative depending on whether the score lies above the mean (in which case it is positive) or below the mean (in which case it is negative) Which means that if Z Score = 1 then that value is one standard deviation from the mean. Meaning in simple terms, it is Z Score that gives you an idea of a value’s relationship to the mean and how far from the mean a data point is.Ī Z Score is measured in terms of standard deviations from the mean. But before we take a look at the formula, let us understand what the Z Score is What is a Z Score?Ī Z Score, also called as the Standard Score, is a measurement of how many standard deviations below or above the population mean a raw score is. It is the Z-Score that gets mapped across the Z-Table and is usually either pre-provided or has to be derived using the Z Score formula. To use the Z-Tables however, you will need to know a little something called the Z-Score.
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