Z-Score in Statistics

Z-Score is used to bring the data to Standard Normal Distribution. The Z-score, or standard score, is the number of standard deviations a given data point that lies above or below the mean.

Key to remember that the mean will always be 0 and the Standard deviation will be 1 always.

Formula:-

Example 1 :-

A Company is creating bulbs with an avg. life of 900 hours, with SD 80 hours. The probability of random bulbs has an avg. life smaller than 1000 hours.

As per the Z-Score table, .89435 is the value and when we multiple it by 100, We get 89.435% are the chances that the avg. life of bulbs is smaller than 1000 hours.

Example 2 :-

There are 10 employees in a team who takes different time to complete a task, How many people can complete the same task in 4 to 5 days.

As per the above example, 15.173% of people will be able to complete the task in 4 to 5 days.

Z-Scores Vs Z-Test

Z-Score is for the population (Formula- (x-mean)/SD)

Z-Test is for the sample population (Formula- (xbar-mean)/SE)

Standard Error(SE):- (SD/root of N)

Difference between Z-score and Z-Test

No such difference between Z-score and Z-test. It’s just we work on data points one by one on the entire data, we call it Z-score. If we are working on the mean of the data then it is called Z-test. Here instead of SD, we use Standard Error.

Let’s take an example for Z-Test

As per Z-table, the value is .48803 which means 48.803% are the changes.