Question

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
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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 $x_1,x_2,\cdots,x_n$. First, find the sum of the weights. The weights of offensive linemen are $356,253,351,259,256,255,263,331,325,311,266,281$.
$n = 12$
$\sum_{i = 1}^{n}x_i=356 + 253+351+259+256+255+263+331+325+311+266+281 = 3507$
The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}=\frac{3507}{12}=292.25$

Step2: Calculate the squared - differences

Calculate $(x_i-\bar{x})^2$ for each $i$. For example, when $i = 1$, $(x_1-\bar{x})^2=(356 - 292.25)^2=(63.75)^2 = 4063.5625$. Do this for all $i$ from $1$ to $12$ and sum them up.
$\sum_{i = 1}^{n}(x_i - \bar{x})^2=(356 - 292.25)^2+(253 - 292.25)^2+(351 - 292.25)^2+(259 - 292.25)^2+(256 - 292.25)^2+(255 - 292.25)^2+(263 - 292.25)^2+(331 - 292.25)^2+(325 - 292.25)^2+(311 - 292.25)^2+(266 - 292.25)^2+(281 - 292.25)^2$
$=4063.5625+1540.5625 + 3451.5625+1105.5625+1314.5625+1387.5625+855.5625+1501.5625+1073.5625+351.5625+689.0625+126.5625$
$=16461$

Step3: Calculate the sample variance

The sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i - \bar{x})^2}{n - 1}=\frac{16461}{11}\approx1496.4545$

Step4: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{s^2}=\sqrt{1496.4545}\approx38.7$

Answer:

$38.7$