Answer :
The standard deviation of the weights of the seven students is approximately 7.63 lb.
To calculate the standard deviation of the weights of the seven students, we need to follow a series of steps that involve finding the mean, calculating the deviations from the mean, squaring the deviations, averaging the squared deviations, and finally taking the square root of the average.
Find the mean: Add up all the weights and divide the sum by the number of students (7). In this case, the mean weight is (178 + 182 + 173 + 184 + 172 + 191 + 194) / 7 = 178.71 lb.
Calculate the deviations: For each student, subtract the mean weight from their individual weight. The deviations from the mean are: -0.71, 3.29, -5.71, 5.29, -6.71, 12.29, and 15.29 lb.
Square the deviations: Square each deviation to eliminate negative values. The squared deviations are: 0.5041, 10.8241, 32.6641, 27.9841, 45.0241, 151.0441, and 234.6841 lb^2.
Average the squared deviations: Add up all the squared deviations and divide by the number of students. The average is (0.5041 + 10.8241 + 32.6641 + 27.9841 + 45.0241 + 151.0441 + 234.6841) / 7 = 58.237 lb^2.
Take the square root: Finally, take the square root of the average squared deviation to find the standard deviation. The square root of 58.237 is approximately 7.63 lb. Therefore, the standard deviation of the weights of the seven students is approximately 7.63 lb.
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