Seven students on an intramural team weigh 166 lb, 178 lb, 161 lb, 172 lb, 168 lb, 187 lb, and 165 lb. What is the standard deviation of the weights of these students?

(Round to the nearest tenth.)

Question

25-06-2024
Mathematics

High School

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Seven students on an intramural team weigh 166 lb, 178 lb, 161 lb, 172 lb, 168 lb, 187 lb, and 165 lb. What is the standard deviation of the weights of these students?

(Round to the nearest tenth.)

Answer :

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Final answer:

To calculate the standard deviation, first find the mean of the weights. Subtract this mean from each weight to get the deviation, square each deviation and take the mean of these squares to get the variance. Finally, the square root of the variance gives the standard deviation, which is approximately 9.2 lb.

Explanation:

The calculation of the standard deviation involves a few steps. First, we need to find the average, or mean, of these weights. Add up all the student weights and then divide by the total number of students. For these seven students, their total weight is 1097 lb, so the average weight is approximately 157 lb (rounded to the nearest lb).

Next, subtract the mean from each student's weight to calculate the deviation for each weight. Then, square each deviation and average these squared deviations. This is the variance. The variance of these weights is approximately 84.86 lb2.

Lastly, take the square root of the variance to find the standard deviation. The standard deviation of these weights is approximately 9.2 lb (rounded to the nearest tenth lb).

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Seven students on an intramural team weigh 166 lb, 178 lb, 161 lb, 172 lb, 168 lb, 187 lb, and 165 lb. What is the standard deviation of the weights of these students? (Round to the nearest tenth.)

Answer :

Final answer:

Explanation:

Other Questions

Seven students on an intramural team weigh 166 lb, 178 lb, 161 lb, 172 lb, 168 lb, 187 lb, and 165 lb. What is the standard deviation of the weights of these students?

(Round to the nearest tenth.)