Questions: Heavy football players: Following are the weights, in pounds, for samples of offensive and defensive linemen on a professional football team at the beginning of a recent year. Offense: 289, 337, 275, 269, 263, 291, 321, 352, 279, 270, 269, 302 Defense: 250, 290, 273, 355, 275, 320, 320, 360, 345, 259, 334 (a) Find the sample standard deviation for the weights for the offensive linemen. Round the answer to at least one decimal place. The sample standard deviation for the weights for the offensive linemen is 29.1 pounds. (b) Find the sample standard deviation for the weights for the defensive linemen. Round the answer to at least one decimal place.

Heavy football players: Following are the weights, in pounds, for samples of offensive and defensive linemen on a professional football team at the beginning of a recent year. Offense: 289, 337, 275, 269, 263, 291, 321, 352, 279, 270, 269, 302 Defense: 250, 290, 273, 355, 275, 320, 320, 360, 345, 259, 334 (a) Find the sample standard deviation for the weights for the offensive linemen. Round the answer to at least one decimal place. The sample standard deviation for the weights for the offensive linemen is 29.1 pounds. (b) Find the sample standard deviation for the weights for the defensive linemen. Round the answer to at least one decimal place.

Transcript text: Heavy football players: Following are the weights, in pounds, for samples of offensive and defensive linemen on a professional football team at the beginning of a recent year. Offense: 289, 337, 275, 269, 263, 291, 321, 352, 279, 270, 269, 302 Defense: 250, 290, 273, 355, 275, 320, 320, 360, 345, 259, 334 (a) Find the sample standard deviation for the weights for the offensive linemen. Round the answer to at least one decimal place. The sample standard deviation for the weights for the offensive linemen is 29.1 pounds. (b) Find the sample standard deviation for the weights for the defensive linemen. Round the answer to at least one decimal place.

Solution

Solution Steps

Step 1: Calculate the Mean

To find the mean \( \mu \) of the weights for the defensive linemen, we use the formula:

\[ \mu = \frac{\sum x_i}{n} \]

where \( \sum x_i \) is the sum of all weights and \( n \) is the number of weights. The sum of the weights is \( 3381 \) and there are \( 11 \) weights:

\[ \mu = \frac{3381}{11} = 307.4 \]

Step 2: Calculate the Variance

The variance \( \sigma^2 \) is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} \]

Substituting the values, we find:

\[ \sigma^2 = 1564.5 \]

Step 3: Calculate the Standard Deviation

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{1564.5} = 39.6 \]