Final answer:
a. The mean weight of the 9 defensive linemen is 289.44 pounds. b. The median weight of the 9 defensive linemen is 280 pounds. c. The first quartile of the 9 defensive linemen is 275 pounds. d. The standard deviation of the 9 defensive linemen's weights is approximately 27.66 pounds.
Step-by-step explanation:
a. To find the mean, we add up all the weights and divide by the number of weights. So, the mean is (275 + 300 + 300 + 315 + 345 + 260 + 275 + 280 + 250)/9 = 289.44 pounds.
b. To find the median, we arrange the weights in ascending order and find the middle value. In this case, the weights arranged in ascending order are: 250, 260, 275, 275, 280, 300, 300, 315, 345. The median is 280 pounds.
c. To find the first quartile, we arrange the weights in ascending order and find the median of the lower half. In this case, the weights arranged in ascending order are: 250, 260, 275, 275, 280, 300, 300, 315, 345. The first quartile is the median of the lower half, which is 275 pounds.
d. To find the standard deviation, we can use the formula:
σ = sqrt(Σ(x - μ)^2 / n)
where σ is the standard deviation, Σ is the sum of the squared differences from the mean, x is each individual weight, μ is the mean, and n is the number of weights. Calculating the standard deviation for this set of weights gives us approximately 27.66 pounds.