Question

heavy football players: following are the weights, in pounds, for offensive and defensive linemen on a professional football team at th year. offense: 356 253 351 259 256 255 263 331 325 311 266 281 defense: 277 309 300 286 329 283 270 352 323 270 355 358 send data to excel part: 0 / 3 part 1 of 3 (a) find the sample standard deviation for the weights of the offensive linemen. round the answer to at least one decimal place. the sample standard deviation for the weights of the offensive linemen is lb.

Explanation:

Step1: Calculate the mean

Let the weights of offensive linemen be $x_1,x_2,\cdots,x_n$. Here $n = 12$, and $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
$\sum_{i=1}^{12}x_i=356 + 253+351+259+256+255+263+331+325+311+266+281 = 3400$.
$\bar{x}=\frac{3400}{12}\approx283.33$.

Step2: Calculate the squared - differences

$(x_1-\bar{x})^2=(356 - 283.33)^2=(72.67)^2 = 5281.9289$.
$(x_2-\bar{x})^2=(253 - 283.33)^2=(- 30.33)^2 = 920.9089$.
$\cdots$
$(x_{12}-\bar{x})^2=(281 - 283.33)^2=(-2.33)^2 = 5.4289$.

Step3: Calculate the sum of squared - differences

$\sum_{i = 1}^{n}(x_i-\bar{x})^2=5281.9289+920.9089+\cdots+5.4289$.
$\sum_{i = 1}^{12}(x_i - \bar{x})^2=14879.3332$.

Step4: Calculate the sample variance

The sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}$.
$s^2=\frac{14879.3332}{11}\approx1352.6667$.

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{s^2}$.
$s=\sqrt{1352.6667}\approx36.8$.

Answer:

$36.8$