Find the standard derivative

Question

ScanSolve AI Tutor · Accepted Answer

To find the standard deviation, we use the formula:

\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{N}}

where $x_i$ are the individual data points, $\bar{x}$ is the mean, and $N$ is the number of data points.
The given data points are $4, 5, 6$ .

Calculate the mean ( $\bar{x}$ ).
The number of data points $N = 3$ .
$\bar{x} = \frac{4 + 5 + 6}{3} = \frac{15}{3} = 5$
Calculate the squared difference of each data point from the mean, $(x_i - \bar{x})^2$ .
For $x_1 = 4$ : $(4 - 5)^2 = (-1)^2 = 1$
For $x_2 = 5$ : $(5 - 5)^2 = (0)^2 = 0$
For $x_3 = 6$ : $(6 - 5)^2 = (1)^2 = 1$
Sum the squared differences.
$\sum (x_i - \bar{x})^2 = 1 + 0 + 1 = 2$
Substitute the values into the standard deviation formula and calculate.
$\sigma = \sqrt{\frac{2}{3}}$ $\sigma \approx \sqrt{0.6667}$ $\sigma \approx 0.8165$
The standard deviation is:
$0.8165$

Answer