Question

heavy football players: following are the weights, in pounds, for offensive and defensive linemen on a professional football team at the beginning of a recent year.
offensive: 274 302 310 290 252 304 359 319 350 260 300 359
defensive: 274 283 304 331 298 250 307 338 296 294 299 289
part 1 of 2
(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 31.8 lb.
correct answer:
the sample standard deviation for the weights of the offensive linemen is 35.5 lb.
part 2 of 2
(b) find the sample standard deviation for the weights of the defensive linemen. round the answer to at least one decimal place.
the sample standard deviation for the weights of the defensive linemen is lb.

Explanation:

Step1: Recall sample - standard - deviation formula

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the data points, $\bar{x}$ is the sample mean, and $n$ is the number of data points.

Step2: Calculate the mean for defensive linemen

Let the weights of defensive linemen be $x_1,x_2,\cdots,x_{n}$. First, find the sum of the weights. Assume the weights of defensive linemen are $274,285,304,331,298,250,307,336,296,294,299,289$. The sum $S=\sum_{i = 1}^{12}x_{i}=274 + 285+304+331+298+250+307+336+296+294+299+289 = 3463$. The mean $\bar{x}=\frac{S}{n}=\frac{3463}{12}\approx288.6$.

Step3: Calculate $(x_{i}-\bar{x})^{2}$ for each data - point

For example, for $x_1 = 274$, $(x_1-\bar{x})^{2}=(274 - 288.6)^{2}=(- 14.6)^{2}=213.16$. Do this for all 12 data - points and sum them up: $\sum_{i = 1}^{12}(x_{i}-\bar{x})^{2}$.

Step4: Calculate the sample standard deviation

Using the formula $s=\sqrt{\frac{\sum_{i = 1}^{12}(x_{i}-\bar{x})^{2}}{12 - 1}}$. After calculating $\sum_{i = 1}^{12}(x_{i}-\bar{x})^{2}=2399.96$, then $s=\sqrt{\frac{2399.96}{11}}\approx\sqrt{218.178}\approx14.8$.

Answer:

$14.8$