Z score (Part 1)

What if I tell you a secret? The secret of how data is distributed in any situation.

Let us start. The mean will be the central point here.

Let us assume if a dataset A is : 10, 12, 14, 16, 19.

Dataset B is: 10, 200, 350, 600, 900.

Now both mean and SD of B is higher than A.

If the dataset C is: 10, 30, 40, 60.

Dataset D is: 31,33,36,40.

Now the mean of dataset C and dataset D are same (35). But what about standard deviation? Are they same? No, the SD of dataset C is higher than dataset D.

So to understand the distribution of data we need both mean and also standard deviation.

While the mean conveys the central point, SD tells us the spread of the data.

Next concept is Z score. What is Z score? In simple words, Z score combines both mean and standard deviation of the data.

Z = (x-mean)/standard deviation.

What is x here? x is a value.

Now let us understand Z scores with example. For example, if the mean is, let’s say 20, and SD is 2, then the Z score for x=20 is 0.

But if the value of x is far away from the mean, let us say x is 30, then the Z score is 5.

Similarly, if the value of x is on the lower side, that is, let us say x is 10, then also Z score is -5, that is minus 5.

(to be continued)