Q. 6.88 - Elementary Statistics

Question

State the empirical rule as specialized to variables.

Step-by-Step Solution

Answer

The percentage that is within one standard deviation of the mean is roughly $68.26\%$.

The percentage within two standard deviations of the mean is $95.44$ per cent.

Around $99.74$ per cent are within three standard deviations of the mean.

Step 1: Concept introduction

The quantity of one variable in algebraic equations is typically reliant on the position of another. If the data tuple isn't declared precisely, the variable's beginning value reflects the default value.

Step 2: Explanation

Normal distributions have a bell shape to them. As a result, the empirical rule is as follows:

For the distributed variable with a bell shape,

- The percentage of observations that are within one standard deviation of the mean is roughly $68.26\%$.

- The percentage of observations that are within two standard deviations of the mean is $95.44\%.$

- Around  of observations are within three standard deviations of the mean.