STANDARDIZE()

Syntax. STANDARDIZE(x,mean,standard_dev)

Definition. This function returns the standardized value of a distribution characterized by an average value and a standard variance.

Arguments

• x (required). The value you want to standardize

• mean (required). The arithmetic mean of the distribution

• standard_dev (required). The standard deviation of the distribution

Note

If standard_dev is less than or equal to 0, the function returns the #NUM! error.

Background. In statistics, the standardization is the transformation of differently scaled number values in a consistent value range from 0 to 1 to compare distributed values.

The standard normal distribution is a type of continuous probability distribution. The special meaning of the normal distribution is based on the central limit theorem that states that a sum of n independent identical distributed random variables is normal distributed at the limit.

See Also

You will find more information about (standard) normal distributions in the description of NORM.DIST().

A standardized normal distribution has the mean 0 and the standard deviation 1. The STANDARDIZE() function returns the standardized value x of a normal distribution with a known mean and standard deviation. The equation for a standardized value is:

Example. You are a light bulb manufacturer and want to analyze the performance of light bulbs. You have already entered the measurements in an Excel table (see Figure 12-130).

Figure 12-130. The measurement results.

You have also calculated the average life cycle and the associated standard deviation, as shown in Figure 12-131.

Figure 12-131. Mean and standard deviation of the performance.

You use the STANDARDIZE() function to standardize all measured values. What arguments does this function require?

• x = distribution values (measured performance)

• mean = 2000 (F6)

• standard_dev = 579 (G6)

Figure 12-132 shows the results.

Figure 12-132. Calculating the standardized values with the STANDARDIZE() function.

Using the STANDARDIZE() function, you generated all standardized distribution values.

Tip

If you specify absolute cell references for the mean and standard_dev arguments, you have to enter the formula only once for any distribution value. Then you can copy the formula for the other values. To specify an absolute cell reference, press the F4 key.

See Also

NORM.DIST(), NORM.INV(), NORM.S.DIST(), NORM.S.INV(), Z.TEST()

Sample Files

Use the STANDARDIZE worksheet in the Probability.xls or Probability.xlsx sample file. The sample files are found in the Chapter12 folder. For more information about the sample files, see the section titled Using the Sample Files.