 ## Standardize in Excel – Let’s compare apples with oranges

Can you compare apples with oranges? Generally speaking, the answer is no.  However, if we use standard deviation as a measure, then we can.  Using standard deviation to compare data with different units is called standardizing.  By standardizing data, you are calculating the Z score.  Standardized values have no units and hence allow you to compare apples with oranges. In Excel, this is easily done using Standardize.

### What is Z Score?

Z scores allow us to compare datasets measured in different units.  Z score is how many standard deviations above or below average a data point is.

For any dataset the average Z score will be = 0 and the standard deviation of Z Scores =1.  Any Z score above 2 or below -2 is an outlier

The formula for Z score is

(X – mean of data) / Standard deviation of data

Where X is the value you wish to solve for

In Excel the Standardize function will calculate Z Scores.  Its syntax is

=STANDARDIZE (x, mean, standard deviation)

### Example How to calculate Z Score in Excel using Standardize

You are told the general mean weight of a mango is 10 oz with a standard deviation of 1.75.  you are also told in general the mean weight of a banana is 7oz with a standard deviation if 2.2.  You buy a banana and a mango and both weigh 9 oz.  Which is bigger?

Doing this manually we must standardize the numbers by calculating a Z score to make a comparison using the formula Z= (X – mean of data) / Standard deviation of data

Mango = (9-10) / 1.75 = -0.571

Banana = (9-7) / 2.2 = 0.909

As the Z score for bananas is larger, we can say the banana is larger than the orange.

In Excel this can be solved using the Standardize function.  The syntax for Standardize is

=STANDARDIZE (x, mean, standard deviation)

Where we are solving for x given the mean and standard deviation.  You can see from the image how these values can be easily plugged into the Standardize function.

### Earn and Learn Activity – Standardize in Excel – Which is bigger, the apple or the orange?

You buy and apple and an orange, both weigh 12oz.  In general, the mean weight for apples is 8oz with a standard deviation of 2 and in general the mean eight for oranges is 10.5oz with a standard deviation of 1.5

Which is bigger, the apple or orange?

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Which is bigger, the apple or the orange?