Question

a veterinarian weighed a sample of 6 puppies. here are each of their weights (in kilograms): 1, 2, 7, 7, 10, 15. the mean of these weights is $\bar{x}=7$ kg. what is the standard deviation? round your answer to two decimal places. $s_xapproxsquare$ kg

Explanation:

Step1: Recall the formula for sample standard - deviation

The formula for the sample standard deviation $s_x=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$, where $n$ is the sample size, $x_i$ are the individual data - points, and $\bar{x}$ is the sample mean. Here, $n = 6$ and $\bar{x}=7$.

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

For $x_1 = 1$: $(1 - 7)^2=(-6)^2 = 36$
For $x_2 = 2$: $(2 - 7)^2=(-5)^2 = 25$
For $x_3 = 7$: $(7 - 7)^2=0^2 = 0$
For $x_4 = 7$: $(7 - 7)^2=0^2 = 0$
For $x_5 = 10$: $(10 - 7)^2=3^2 = 9$
For $x_6 = 15$: $(15 - 7)^2=8^2 = 64$

Step3: Calculate the sum $\sum_{i = 1}^{n}(x_i-\bar{x})^2$

$\sum_{i = 1}^{6}(x_i-\bar{x})^2=36 + 25+0 + 0+9 + 64=134$

Step4: Calculate the sample standard deviation

$s_x=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}=\sqrt{\frac{134}{6 - 1}}=\sqrt{\frac{134}{5}}=\sqrt{26.8}\approx5.18$

Answer:

$5.18$