Question

in an engineering class, students took 10, 13, 12, 17, 15 hours to design their models. what is the standard deviation? the standard deviation is (round to the nearest whole number as needed.)

Explanation:

Step1: Calculate the mean

First, find the mean $\bar{x}$ of the data - set $\{10,13,12,17,15\}$. The formula for the mean of a sample $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n$ is the number of data - points and $x_{i}$ are the individual data - points. Here, $n = 5$, and $\sum_{i=1}^{5}x_{i}=10 + 13+12+17+15=67$. So, $\bar{x}=\frac{67}{5}=13.4$.

Step2: Calculate the squared differences

Next, find the squared differences $(x_{i}-\bar{x})^{2}$ for each data - point:
For $x_1 = 10$: $(10 - 13.4)^{2}=(-3.4)^{2}=11.56$
For $x_2 = 13$: $(13 - 13.4)^{2}=(-0.4)^{2}=0.16$
For $x_3 = 12$: $(12 - 13.4)^{2}=(-1.4)^{2}=1.96$
For $x_4 = 17$: $(17 - 13.4)^{2}=(3.6)^{2}=12.96$
For $x_5 = 15$: $(15 - 13.4)^{2}=(1.6)^{2}=2.56$

Step3: Calculate the variance

The formula for the sample variance $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$. Here, $\sum_{i = 1}^{5}(x_{i}-\bar{x})^{2}=11.56+0.16+1.96+12.96+2.56 = 29.2$, and $n-1=4$. So, $s^{2}=\frac{29.2}{4}=7.3$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{s^{2}}$. So, $s=\sqrt{7.3}\approx2.7$. Rounding to the nearest whole number, $s = 3$.

Answer:

3