How do you find a standardized value?

As a subject matter expert in statistics, I'm often asked about how to find a standardized value, also known as a z-score. This is a measure of how many standard deviations an element is from the mean. It's a crucial concept in statistics, as it allows us to compare values from different distributions on a common scale. Let's delve into the steps to find a standardized value.
Step 1: Identify the observation (X), the mean (μ), and the standard deviation (σ) in the question. These are the three key components you need to calculate a z-score. The observation is the data point you're interested in, the mean is the average of the dataset, and the standard deviation is a measure of the spread or variability of the dataset.

Step 2: **Plug the values from Step 1 into the formula**. The formula for calculating a z-score is as follows:
\[ z = \frac{X - μ}{σ} \]

Now, let's apply this to the example you've provided. It seems there is a slight error in the formula as presented. The correct formula should be:
\[ z = \frac{X - μ}{σ} \]

Given the values:
- Observation (X) = 520
- Mean (μ) = 420
- Standard Deviation (σ) = 50

We can calculate the z-score as follows:
\[ z = \frac{520 - 420}{50} \]
\[ z = \frac{100}{50} \]
\[ z = 2 \]

This means that the observation is 2 standard deviations above the mean.

Now, let's translate this explanation into Chinese.

Step 1: Identify the observation (X), the mean (--) and the standard deviation (--) in the question. Step 2: Plug the values from Step 1 into the formula: Standardized value = X -C -- / -- = 520 -C 420 / 50.Oct 15, 2014