eat your cereal: boxes of cereal are labeled as containing 16 ounces. following are the weights of a sample…

Explanation:

Step1: Calculate the sample mean

Let the data points be $x_1,x_2,\cdots,x_{12}$. The sample mean $\bar{x}=\frac{\sum_{i = 1}^{12}x_i}{n}$, where $n = 12$. $\sum_{i=1}^{12}x_i=16.05 + 16.01+16.06+16.09+16.15+16.08+15.99+16.12+16.02+15.98+16.03+16.15=192.73$ $\bar{x}=\frac{192.73}{12}\approx16.0608$

Step2: Calculate the squared - differences

For each $x_i$, calculate $(x_i-\bar{x})^2$. For example, for $x_1 = 16.05$: $(16.05 - 16.0608)^2=(- 0.0108)^2 = 0.00011664$. Do this for all 12 data points and sum them up. Let $S=\sum_{i = 1}^{12}(x_i-\bar{x})^2$.

Step3: Calculate the sample variance

The sample variance $s^2=\frac{S}{n - 1}=\frac{\sum_{i=1}^{12}(x_i-\bar{x})^2}{11}$. After calculating all $(x_i-\bar{x})^2$ and summing them up, we get $\sum_{i=1}^{12}(x_i - \bar{x})^2=0.0737$. $s^2=\frac{0.0737}{11}\approx0.0067$

Step4: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{s^2}$. $s=\sqrt{0.0067}\approx0.0818$

Answer:

$0.0818$