Question

test 1
score: 6.72/10 answered: 7/10
progre
question 8
a survey of a population collected the data below. calculate the standard deviation, to one decimal place.
question help: video

Explanation:

Step1: Calculate the mean

The formula for the mean $\mu$ of a population is $\mu=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $x_1 = 27$, $x_2=6$, $x_3 = 7$, $x_4=3$, $x_5 = 30$, and $n = 5$.
$\mu=\frac{27 + 6+7+3+30}{5}=\frac{73}{5}=14.6$

Step2: Calculate the squared - differences from the mean

The formula for the squared - difference is $(x_i-\mu)^2$.
For $x_1 = 27$: $(27 - 14.6)^2=(12.4)^2 = 153.76$
For $x_2 = 6$: $(6 - 14.6)^2=(- 8.6)^2=73.96$
For $x_3 = 7$: $(7 - 14.6)^2=(-7.6)^2 = 57.76$
For $x_4 = 3$: $(3 - 14.6)^2=(-11.6)^2=134.56$
For $x_5 = 30$: $(30 - 14.6)^2=(15.4)^2 = 237.16$

Step3: Calculate the variance

The formula for the population variance $\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_i-\mu)^2}{n}$
$\sum_{i = 1}^{5}(x_i-\mu)^2=153.76+73.96 + 57.76+134.56+237.16=657.2$
$\sigma^{2}=\frac{657.2}{5}=131.44$

Step4: Calculate the standard deviation

The formula for the population standard deviation $\sigma=\sqrt{\sigma^{2}}$
$\sigma=\sqrt{131.44}\approx11.5$

Answer:

$11.5$