Question

suppose you made 5 measures of your walking times and got the following values: 5.6 s, 5.9 s, 5.5 s, 5.6 s, and 5.8 s what is the standard deviation (in seconds) of this sample? you may either do this by hand or use your favorite math tool. add your answer integer, decimal, or e notation allowed

Explanation:

Step1: Calculate the mean ($\bar{x}$)

The formula for the mean is $\bar{x} = \frac{\sum_{i = 1}^{n} x_i}{n}$, where $x_i$ are the data points and $n$ is the number of data points.
Here, $x_1 = 5.6$, $x_2 = 5.9$, $x_3 = 5.5$, $x_4 = 5.6$, $x_5 = 5.8$ and $n = 5$.
$\sum_{i = 1}^{5} x_i=5.6 + 5.9+5.5 + 5.6+5.8 = 28.4$
$\bar{x}=\frac{28.4}{5}=5.68$

Step2: Calculate the squared differences from the mean

For each data point $x_i$, calculate $(x_i-\bar{x})^2$:

• For $x_1 = 5.6$: $(5.6 - 5.68)^2=(- 0.08)^2 = 0.0064$
• For $x_2 = 5.9$: $(5.9 - 5.68)^2=(0.22)^2=0.0484$
• For $x_3 = 5.5$: $(5.5 - 5.68)^2=(-0.18)^2 = 0.0324$
• For $x_4 = 5.6$: $(5.6 - 5.68)^2=(-0.08)^2=0.0064$
• For $x_5 = 5.8$: $(5.8 - 5.68)^2=(0.12)^2 = 0.0144$

Step3: Calculate the sum of squared differences

$\sum_{i = 1}^{5}(x_i - \bar{x})^2=0.0064+0.0484 + 0.0324+0.0064+0.0144=0.108$

Step4: Calculate the sample variance ($s^2$)

The formula for sample variance is $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}$
Here, $n=5$, so $n - 1=4$
$s^2=\frac{0.108}{4}=0.027$

Step5: Calculate the sample standard deviation ($s$)

The sample standard deviation is the square root of the sample variance, $s=\sqrt{s^2}$
$s=\sqrt{0.027}\approx0.1643$

Answer:

$0.1643$ (or approximately $0.16$ if rounded to two decimal places)