Question

what is the standard deviation of the following sample: 45, 59, 49, 52, 55?
hint: use the following.
sum of squares

x	(x - x̄)	(x - x̄)²
59
49
52
55
x̄ =		σ =

s = √(σ(x - x̄)² / (n - 1))
23.2
4.82
5.39
29
38.67

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{45 + 59+49+52+55}{5}=\frac{260}{5}=52$

Step2: Calculate $(x - \bar{x})$ and $(x - \bar{x})^2$ for each $x$

For $x = 45$: $(45 - 52)=-7$, $(45 - 52)^2 = 49$
For $x = 59$: $(59 - 52)=7$, $(59 - 52)^2 = 49$
For $x = 49$: $(49 - 52)=-3$, $(49 - 52)^2 = 9$
For $x = 52$: $(52 - 52)=0$, $(52 - 52)^2 = 0$
For $x = 55$: $(55 - 52)=3$, $(55 - 52)^2 = 9$

Step3: Calculate the sum of squares $\sum(x - \bar{x})^2$

$\sum(x - \bar{x})^2=49 + 49+9+0+9=116$

Step4: Calculate the standard deviation

$n = 5$, and the formula for sample - standard deviation is $s=\sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}$. Substitute $\sum(x - \bar{x})^2 = 116$ and $n = 5$ into the formula:
$s=\sqrt{\frac{116}{5 - 1}}=\sqrt{\frac{116}{4}}=\sqrt{29}\approx5.39$

Answer:

$5.39$