The following list gives the number of hours spent watching television in a week by a group of students: 15, 3, 25, 29, 10, 11, 0, 33.The mean and standard deviation are closest to:

Question

BlackTom AI · Accepted Answer

Mean = sum/n. Sum the data: 15 + 3 + 25 + 29 + 10 + 11 + 0 + 33 = 126. With n = 8, the mean = 126/8 = 15.75, which rounds to 15.8.

For the standard deviation we use the sample standard deviation formula s = sqrt(Σ(xi - x̄)² / (n − 1)). Compute each deviation and its square using x̄ = 15.75:
- 15 − 15.75 = −0.75 → 0.5625
- 3 − 15.75 = −12.75 → 162.5625
- 25 − 15.75 = 9.25 → 85.5625
- 29 − 15.75 = 13.25 → 175.5625
- 10 − 15.75 = −5.75 → 33.0625
- 11 − 15.75 = −4.75 → 22.5625
- 0 − 15.75 = −15.75 → 248.0625
- 33 − 15.75 = 17.25 → 297.5625

Sum of squared deviations = 0.5625 + 162.5625 + 85.5625 + 175.5625 + 33.0625 + 22.5625 + 248.0625 + 297.5625 = 1025.5.

Sample variance = 1025.5 / (8 − 1) = 1025.5 / 7 = 146.5. Therefore s = sqrt(146.5) ≈ 12.103, which rounds to 12.1.

Why this option is correct: the mean 15.75 rounds to 15.8 and the sample standard deviation computed by the (n − 1) denominator gives ≈12.1, matching option c.

Why the other choices are incorrect:
- a (mean = 15.8, s = 11.3): 11.3 is the population standard deviation (using denominator n), not the sample s. The mean is correct but the sd uses the wrong divisor.
- b (mean = 18.0, s = 11.1): the mean 18.0 is incorrect for these data.
- d (mean = 15.7, s = 11.3): the sd is again the population value; the mean rounding to 15.7 is a less accurate rounding of 15.75 than 15.8.

Conclusion: the correct choice is c. mean = 15.8, s = 12.1.

The following list gives the number of hours spent watching television in a week by a group of students: 15, 3, 25, 29, 10, 11, 0, 33.The mean and standard deviation are closest to:单项选择题

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