 ## Basics of Statistics for Data Science: How to calculate Z score

Z score is a statistic used to measure the number of standard deviations above or below the mean of your population. Therefore to calculate your Z score, you will need to calculate the value of the mean and standard deviation of your sample.

The formula for

Z score = (x- µ ) /  σ

Where,

µ is the mean of your sample

σ is the standard deviation of your sample

x is single data point in your population.

We will discuss this with an example. Let us say, there are 5 members in your family. Their Age are x (10, 20, 25 15, 20).

The mean age of your family can be calculated as

µ = (10 + 20 + 25 + 15 + 20) /5 = 18

The standard deviation (σ) is to be calculated in a spread sheet

σ = √(Σ   (x- µ)^2/N

where N is the population size.

Standard deviation (σ) = 5.099

Let us calculate Z score for age 10

Z score = (10 -18) / 5.099 = – 1.57

S

o the person with age 10 is 1.57 standard deviation below the average mean i.e 18 of your family.

You may use this formula for calculating the Z score.