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I might know what's going on. The Z-score is defined as $$ z = \frac{x-\mu}{\sigma} $$ where $\mu$ is the mean and $\sigma$ is the standard deviation(SD).

In your example, $\mu = 30$, $x = 60$ and $\sigma = 2$.

Using the formula directly, the Z-score of your observation is

$$z = \frac{x-\mu}{\sigma} = \frac{60-30}{2} = 15$$

When you solve the equation for $x$, you get the formula, $x = \mu + 15\sigma$. Directly interpreting this formula, you can say that your score, $x$ is 15 SD away from the mean.

On the other hand, you can expand the Z-score formula in this way: $$ z = \frac{x}{\sigma} - \frac{\mu}{\sigma} $$

By rewriting the formula with the calculated Z-score, you get

$$ \begin{align} \frac{x}{\sigma} & = z + \frac{\mu}{\sigma} = 15 +\frac{\mu}{\sigma} \end{align} $$

With this formula, you can describe the score as the score per SD is 15 away from the mean per SD. In this version, all the quantities are unitless.

They are different ways of looking at the same Z-score.

I might know what's going on. The Z-score is defined as $$ z = \frac{x-\mu}{\sigma} $$ where $\mu$ is the mean and $\sigma$ is the standard deviation(SD).

In your example, $\mu = 30$, $x = 60$ and $\sigma = 2$.

Using the formula directly, the Z-score of your observation is

$$z = \frac{x-\mu}{\sigma} = \frac{60-30}{2} = 15$$

When you solve the equation for $x$, you get the formula, $$x = \mu + 15\sigma$$

Directly interpreting this formula, you can say that the score, $x$ is 15 SD away from the mean.

On the other hand, you can expand the Z-score formula in this way: $$ z = \frac{x}{\sigma} - \frac{\mu}{\sigma} $$

By rewriting the formula with the calculated Z-score, you get

$$ \begin{align} \frac{x}{\sigma} & = z + \frac{\mu}{\sigma} = 15 +\frac{\mu}{\sigma} \end{align} $$

With this formula, you can describe the score as the score per SD is 15 away from the mean per SD. In this version, all the quantities are unitless.

They are different ways of looking at the same Z-score.

I might know what's going on. The Z-score is defined as $$ z = \frac{x-\mu}{\sigma} $$ where $\mu$ is the mean and $\sigma$ is the standard deviation(SD).

In your example, $\mu = 30$, $x = 60$ and $\sigma = 2$.

Using the formula directly, the Z-score of your observation is

$$z = \frac{x-\mu}{\sigma} = \frac{60-30}{2} = 15$$

When you expand the formula for $x$, you have $x = \mu + 15\sigma$. Directly interpreting this formula, you can say that your score, $x$ is 15 SD away from the mean.

On the other hand, you can expand the Z-score formula in this way: $$ z = \frac{x}{\sigma} - \frac{\mu}{\sigma} $$

By rewriting the formula with Z-score calculated, you get

$$ \begin{align} \frac{x}{\sigma} & = z + \frac{\mu}{\sigma} = 15 +\frac{\mu}{\sigma} \end{align} $$

With this formula, you can describe your score as your score per SD is 15 away from the mean per SD.

They are different ways of looking at the same Z-score.

I might know what's going on. The Z-score is defined as $$ z = \frac{x-\mu}{\sigma} $$ where $\mu$ is the mean and $\sigma$ is the standard deviation(SD).

In your example, $\mu = 30$, $x = 60$ and $\sigma = 2$.

Using the formula directly, the Z-score of your observation is

$$z = \frac{x-\mu}{\sigma} = \frac{60-30}{2} = 15$$

When you solve the equation for $x$, you get the formula, $x = \mu + 15\sigma$. Directly interpreting this formula, you can say that your score, $x$ is 15 SD away from the mean.

On the other hand, you can expand the Z-score formula in this way: $$ z = \frac{x}{\sigma} - \frac{\mu}{\sigma} $$

By rewriting the formula with the calculated Z-score, you get

$$ \begin{align} \frac{x}{\sigma} & = z + \frac{\mu}{\sigma} = 15 +\frac{\mu}{\sigma} \end{align} $$

With this formula, you can describe the score as the score per SD is 15 away from the mean per SD. In this version, all the quantities are unitless.

They are different ways of looking at the same Z-score.

I might know what's going on. The Z-score is defined as $$ z = \frac{x-\mu}{\sigma} $$ where $\mu$ is the mean and $\sigma$ is the standard deviation(SD).

In your example, $\mu = 30$, $x = 60$ and $\sigma = 2$.

Using the formula directly, the Z-score of your observation is

$$z = \frac{x-\mu}{\sigma} = \frac{60-30}{2} = 15$$

In another words, $x = \mu + 15\sigma$. Directly interpreting this formula, you can say that your score, $x$ is 15 SD away from the mean.

On the other hand, you can expand the Z-score formula in this way: $$ z = \frac{x}{\sigma} - \frac{\mu}{\sigma} $$

By rewriting the formula with Z-score calculated, you get

$$ \begin{align} \frac{x}{\sigma} & = z + \frac{\mu}{\sigma} = 15 +\frac{\mu}{\sigma} \end{align} $$

With this formula, you can describe your score as your score per SD is 15 away from the mean per SD.

They are different ways of looking at the same Z-score.

I might know what's going on. The Z-score is defined as $$ z = \frac{x-\mu}{\sigma} $$ where $\mu$ is the mean and $\sigma$ is the standard deviation(SD).

In your example, $\mu = 30$, $x = 60$ and $\sigma = 2$.

Using the formula directly, the Z-score of your observation is

$$z = \frac{x-\mu}{\sigma} = \frac{60-30}{2} = 15$$

When you expand the formula for $x$, you have $x = \mu + 15\sigma$. Directly interpreting this formula, you can say that your score, $x$ is 15 SD away from the mean.

On the other hand, you can expand the Z-score formula in this way: $$ z = \frac{x}{\sigma} - \frac{\mu}{\sigma} $$

By rewriting the formula with Z-score calculated, you get

$$ \begin{align} \frac{x}{\sigma} & = z + \frac{\mu}{\sigma} = 15 +\frac{\mu}{\sigma} \end{align} $$

With this formula, you can describe your score as your score per SD is 15 away from the mean per SD.

They are different ways of looking at the same Z-score.