Question

ryan went surfing 5 mornings this year. he logged the number of good waves each morning:
9 waves 7 waves 9 waves 1 wave 5 waves
what was the standard deviation of the numbers of good waves?
if the answer is a decimal, round it to the nearest tenth.
standard deviation (σ): waves
submit

Explanation:

Step1: Calculate the mean

The mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
Here, $n = 5$, $x_1=9$, $x_2 = 7$, $x_3=9$, $x_4 = 1$, $x_5=5$.
$\bar{x}=\frac{9 + 7+9+1+5}{5}=\frac{31}{5}=6.2$.

Step2: Calculate the squared - differences from the mean

For $x_1 = 9$: $(9 - 6.2)^2=(2.8)^2 = 7.84$.
For $x_2 = 7$: $(7 - 6.2)^2=(0.8)^2 = 0.64$.
For $x_3 = 9$: $(9 - 6.2)^2=(2.8)^2 = 7.84$.
For $x_4 = 1$: $(1 - 6.2)^2=(-5.2)^2 = 27.04$.
For $x_5 = 5$: $(5 - 6.2)^2=(-1.2)^2 = 1.44$.

Step3: Calculate the variance

The variance formula for a population is $\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n}$.
$\sum_{i = 1}^{5}(x_{i}-\bar{x})^{2}=7.84+0.64 + 7.84+27.04+1.44=44.8$.
$\sigma^{2}=\frac{44.8}{5}=8.96$.

Step4: Calculate the standard deviation

The standard deviation formula is $\sigma=\sqrt{\sigma^{2}}$.
$\sigma=\sqrt{8.96}\approx3.0$.

Answer:

$3.0$