use the formula to find the standard deviation of 3, 4, 6, 9, 13.\nstep 1. find the mean, x.\nstep 2. find…

use the formula to find the standard deviation of 3, 4, 6, 9, 13.\nstep 1. find the mean, x.\nstep 2. find the deviation, or difference, between each data value and the mean, x - x. some of the differences will be negative, and some will be positive.\nstep 3. square each difference, (x - x)^2.\nstep 4. find the sum of the squared differences, σ(x - x)^2.\nstep 5: divide the sum by n - 1. this gives you s^2.\ns^2 = \\frac{1}{n - 1}σ(x - \\bar{x})^2

use the formula to find the standard deviation of 3, 4, 6, 9, 13.\nstep 1. find the mean, x.\nstep 2. find the deviation, or difference, between each data value and the mean, x - x. some of the differences will be negative, and some will be positive.\nstep 3. square each difference, (x - x)^2.\nstep 4. find the sum of the squared differences, σ(x - x)^2.\nstep 5: divide the sum by n - 1. this gives you s^2.\ns^2 = \\frac{1}{n - 1}σ(x - \\bar{x})^2

Answer

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{3 + 4+6+9+13}{5}=\frac{35}{5} = 7$.

Step2: Find the deviation

For $x = 3$, $x-\bar{x}=3 - 7=-4$; for $x = 4$, $x-\bar{x}=4 - 7=-3$; for $x = 6$, $x-\bar{x}=6 - 7=-1$; for $x = 9$, $x-\bar{x}=9 - 7 = 2$; for $x = 13$, $x-\bar{x}=13 - 7=6$.

Step3: Square the deviation

For $x = 3$, $(x - \bar{x})^2=(-4)^2 = 16$; for $x = 4$, $(x - \bar{x})^2=(-3)^2 = 9$; for $x = 6$, $(x - \bar{x})^2=(-1)^2 = 1$; for $x = 9$, $(x - \bar{x})^2=2^2 = 4$; for $x = 13$, $(x - \bar{x})^2=6^2 = 36$.

Step4: Sum of squared deviations

$\sum(x-\bar{x})^2=16 + 9+1+4+36=66$.

Step5: Calculate the variance

$n = 5$, so $s^{2}=\frac{\sum(x-\bar{x})^2}{n - 1}=\frac{66}{4}=16.5$.

Step6: Calculate the standard - deviation

$s=\sqrt{s^{2}}=\sqrt{16.5}\approx4.06$.

Answer:

The standard deviation is approximately $4.06$.