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# How to find how many standard deviations are away from the mean?

The statement signifies the magnitude of the standard deviation deferred from the mean of the data.

## Answer: The value of standard deviation, away from mean is calculated by the formula, X = µ ± Zσ

The standard deviation can be considered as the average difference (positive difference) between an observation and the mean.

**Explanation:**

Let Z denote the amount by which the standard deviation differs from the mean.

Therefore, Z = (X - µ)/**σ**

where µ denotes the mean,

**σ **denotes the standard deviation,

X is the value of standard deviation away from the mean.

⇒ X = µ **±** Z**σ**

Let us try to understand the above value of X using the graph given below and study at certain points.

( Standard deviation away from the mean i.e center of the graph )

For example,

µ - 2**σ** (which shows two standard deviations below the mean)

µ - **σ **(which shows 1 standard deviation below the mean)

µ (which shows 0 standard deviations from the mean or exact mean)

µ + **σ **(which shows 1 standard deviation above the mean)

### Hence, the value of standard deviation, away from the mean is calculated by the formula, X = µ ± Zσ.

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