Answer :
Final answer:
To find the standard deviation of the weights of the seven students, you need to calculate the mean, find the deviation from the mean, square each deviation, calculate the variance, and then find the square root of the variance.
Explanation:
To find the standard deviation of the weights of the seven students, we need to follow these steps:
Calculate the mean weight by adding up all the weights and dividing by the number of students (183+178+178+189+168+187+170 = 1253, 1253/7 = 179).
Find the deviation of each weight from the mean by subtracting the mean from each weight (183-179 = 4, 178-179 = -1, 178-179 = -1, 189-179 = 10, 168-179 = -11, 187-179 = 8, 170-179 = -9).
Square each deviation (4² = 16, (-1)² = 1, (-1)² = 1, 10² = 100, (-11)² = 121, 8² = 64, (-9)² = 81).
Calculate the variance by adding up the squared deviations and dividing by the number of students (16+1+1+100+121+64+81 = 384, 384/7 = 54.857).
Take the square root of the variance to find the standard deviation (√54.857 ≈ 7.406).
Therefore, the standard deviation of the weights of these students is approximately 7.4 pounds.
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