Answer :
Final answer:
The standard deviation of the weights of the seven students is calculated by finding the mean weight and subtracting this from each weight to give the deviations. These deviations are squared, added together and then divided by the number of students minus one. The square root of this result is the standard deviation: approximately 10.16lb.
Explanation:
To calculate the standard deviation of the weights of the students, we first need to find the mean (average) weight. Add up all the weights and divide by the number of students. This gives us the mean weight.
The weights are 183lb, 183lb, 178lb, 189lb, 173lb, 192lb, and 162 lb. Adding these together gives us 1,260lb. There are seven students, so dividing 1,260 by 7 gives us a mean weight of 180lb.
Next, subtract the mean from each weight to get the deviation for each weight. Square these deviations, add them all together and divide by the number of students-1. Finally, take the square root of this number to find the standard deviation.
The deviations are: 3, 3, -2, 9, -7, 12, -18
Squaring these deviations gives: 9, 9, 4, 81, 49, 144, 324
Adding these together gives 620. Divide this by 6 (the total number of students - 1) gives ~103.33, and the square root of 103.33 is approximately 10.16lb.
So the standard deviation of the student's weights is approximately 10.16lb.
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